That's an interesting line that FreeRepublic presents in Reply #12. It wasn't familiar to me, so I looked in a few references and found some coverage (at least up to 10.Bxc4) in a number of works, including the 70s-era Queen's Gambit books by Samarian and Pachman, ECO D (2nd Edition, 1987), Queen's Gambit: Orthodox Defence (Polugayevsky, 1988), NCO (1999) and Learn the Queen's Gambit (Karpov & Kalinichecko, 2018). These authors mostly use the traditional move order for the Orthodox Variation: 1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.Bg5 Be7 5.e3 0-0 6.Nf3 Nbd7 7.Rc1 c6 8.Bd3. Now 8...dxc4 9.Bxc4 h6 10.Bh4 tranposes into the line from Reply #12, as does 8...h6 9.Bh4 dxc4 10.Bxc4. Of course, after 8...dxc4 9.Bxc4, Capablanca's freeing manoeuver (9...Nd5) leads to the main line of the Orthodox. Thus, the line with ...h6 can be considered a side branch of the Orthodox Variation.

Samarian notes that ...h6 is a good preparatory move for an extended fianchetto. Thus, after 10.Bxc4 in the line from Reply #12, all of the aforementioned books give 10...b5 as the main move. Apparently, omitting ...h6, as in 8.Bd3 dxc4 9.Bxc4 b5 10.Bd3 a6, allows 11.e4, which was considered good for White. In contrast, after insertion of ...h6 and Bh4, the line 10...b5 11.Bd3 a6 12.e4 is now met with the tactic 12...Nxe4! with the continuation 13.Bxe4 Bxh4 14.Bxc6 Ra7 15.0-0 Nb6= (Euwe-Alekhine, Match (28) 1935). Without the inclusion of ...h6 and Bh4, White could meet ...Nxe4 with Nxe4, adding another protector to the bishop on g5. Hence the need to add ...h6 at some point in order to play the extended fianchetto.

Along with being the main move in books,  10...b5 is also the most popular answer to 10.Bxc4 in the Mega database, with nearly 700 games. Thus, it's not exactly an obscure move. Along with Alekhine in the game cited above, Capablanca also played 10...b5 as Black, at Margate 1936 in games vs Thomas and Stahlberg. From a theoretical point of view, a key game is Fischer-Spassky, Match (12) 1972, which went 10...b5 11.Bd3 a6 12.a4 bxa4 13.Nxa4 Qa5+ 14.Nd2 Bb4 15.Nc3 c5 16.Nb3 Qd8 17.0-0 cxd4 18.Nxd4 Bb7 19.Be4 when most of the authors gave White a small edge. On the other hand, Stockfish evaluates this position as equal.

Ruslan Scherbakov's March 2008 update to the ChessPublishing 1.d4 d5 2.c4 section is a bit unusual since, instead of analyzing recent contests, he covers games that are theoretically important to the classical approach to the QGD with ...Nbd7. Among these games are three involving 10...b5. In his notes to Kharitonov-Nenashev, Omsk 1985, Scherbakov states that, "As a rule, the inclusion of ...h7-h6 is useful for Black in most QGD positions. However, here it almost forces him to play a rather unusual setup since the normal simplifying strategy of 10...Nd5 no longer achieves the desired effect due to 11.Bg3." After 11.Bd3 a6, he comments, "So Black is playing a strange mixture of the Queen's Gambit on the K-side and the Meran on the opposite flank!"

In the same update, Scherbakov also includes the Fischer-Spassky game. Unlike other annotators who attributed a slight edge to White after 19.Be4, Scherbakov says, "Black was accurate in the opening, and White was unable to obtain any serious pressure". In addition, his update includes Kamsky-Salov, Candidates (3) 1995, where Kamsky "introduced a small innovation on move 23" achieving better results than in Fischer-Spassky. My research found the move 23 "innovation" was already published in ECO D a few years before Kamsky-Salov. Nonetheless, it led to a difficult defense for Black, who succumbed to a kingside attack. Salov missed an opportunity or two to equalize, which suggests that 10...b5 may present some practical challenges for the second player.

The preceding was admittedly a lengthy digression into 10...b5, but the continuation 11.Bd3 a6 is quite common. Since it would seem that in many cases, ...b5 and ...a6 can be played in the opposite order, the information has some relevance to the 10...a6 line in reply #12.

Moving to 10...a6 itself, a search of the Mega database finds the move to be much less common, with only 46 games found. Despite the low number, ChessBase marks 10...a6 as a "hot" line. Interestingly, 10...b5 also receives this designation. If anything, the "hot" symbol for 10...b5 is even larger, suggesting that it is more fashionable. However, 10...a6 scores better for Black.

Likely reflecting the relatively scarcity of 10...a6, Polugayevsky's Queen's Gambit: Orthodox Defence was the only book that I found with coverage of this move. He calls it "an alternative which is used occasionally", giving two continuations. He notes that 11.a4 ("a satisfactory answer" - Polugayevsky) 11...b5 12.Bd3 transposes to 10...b5 and the Fischer-Spassky game. Polugayevsky also gives a more independent line: 11...c5 (instead of 11...b5) 12.0-0 cxd4 13.exd4 with a variation of the Queen's Gambit Accepted that he feels favors White since the Black knight stands worse on d7 than on its usual c6 square in the QGA. 

ChessPublishing analyzed 10...a6 on a couple of occasions. In his notes to Cheparinov-Sherefiev, European CC Final 2021, Justin Tan gives the variation 11.a4 c5 12.Qb3⩲ when "Black has development problems.". He adds the sample continuation 12...b6 13.Ne5 cxd4 14.Nc6 Qe8 15.exd4. Black certainly looks rather congested here, but the silicon seer says the position is equal.

Milos Pavlovic also looked at 10...a6 for ChessPublishing in his notes to Shankland-Zherebukh, ch-USA St Louis 2018. He gives 11.a3 (Pavlovic mentions that 11.a4 and 11.Bd3 are critical moves to be assessed, but he doesn't go any further) 11...b5 12.Ba2 Bb7 13.0-0 c5! Here Pavlovic says, "Black is already fine." Stockfish concurs, evaluating the position as =. Note that White didn't piut any particular pressure on Black, so the second player was able to execute his plan of seizing space on the queenside while opening the long diagonal for the light-squared bishop.

Just before posting, I thought I should also check on the use of 10...a6 in correspondence play. It's a bit surprising that a significant number of games (70) with 10...a6 were found in the UltraCorr database. The great majority were played since 2010 with a noticeable period of popularity around the early years of the 2010s. Black did decently, scoring 11 wins, 11 losses, and 48 draws. About a third of the games (24 to be exact) followed Polugayevsky's QGA line: 10...a6 11.a4 c5 12.0-0 cxd4 13.exd4. Despite his comment about the poor positioning of the knight on d7, Black did well with 5 wins, 4 losses, and 15 draws. A common followup was 13...Nb6 14.Ba2 (or 14.Bb3) when Black then brings the knight from b6 to d5 and develops the c8-bishop via d7 and c6 with classic play against the IQP. A cursory review of the games shows White often employed common IQP themes such as setting up a queen + bishop battery on the b1-h7 diagonal and bringing a knight to e5. However, Black seems to have sufficient resources to hold the balance, at least in CC. Apparently it's a bit different situation in OTB. In the 51 games in the Mega database with the position after 13.cxd4, White scored 22 wins vs 10 losses and 19 draws (about 62%). 

In reviewing the data, I get the impression that 10...a6 is useful for awaiting White's disclosure of his plans. As FreeRepublic notes, Black can play ...b5 or ...c5 depending on the circumstances. In the right situation, Black can play ...b5 without hindrance, getting something like the ideal setup of Shankland-Zherebukh. On the other hand, 11.a4 c5, while satisfactory in principle, may pose some practical challenges for Black in OTB play. Familiarity with play against the IQP would seem to be helpful here.

Nietzsche wrote on 05/26/06 at 08:02:06:

I agree that it depends on the variation.

The Tartakover has a good reputation, scores well in games, and is engine approved. Of course, you can expect that players of the White pieces will excercise their ingenuity to give Black new challenges. It is positionally well-motivated but tactics will crop up. The positions are usually equal, but not necessarily easy to play.

The Cambridge Springs variation seems tactically motivated. With one move, 6...Qa5, Black breaks a pin and inflicts a pin! From a positional viewpoint, developing the queen so early seems suspect. I think it is playable, but White is often a little better.

The Manhatan variation has had its ups and downs but is currently looking good to me.
 
The Orthodox variation has never had good overall statistics.  However move order subtleties or new interpretations may keep this old variation young.

1. d4 d5 2. c4 e6 3. Nc3 Nf6 4. Bg5 Be7 5. e3 Nbd7 6. Nf3 c6 7. Rc1 h6 8. Bh4 O-O 9. Bd3 dc4 10. Bc4 a6!?

Depending on circumstances, Black can play ...b5 or ...c5 on the next move. It looks like Black will get a good and lively game.

Okay, my last post was sort of contradictory because I talked about the super-gm games and the statistics they generate and then I went on to recommend the study of a bunch of Kasparov games! sorry about that! lol. Anyway, I know a guy at my club who is very sharp tactically and he plays the Sicilian Dragon vs. e4 and guess what...the QGD vs. d4 and man he comes down hard on those unwary d4 players. Good Luck with QGD.

Of course no opening is foolproof.

Openings just happen to be independent of the result in a chess game since there are many paths and blunders for players to choose from.

The simple answer seems to be that the QGD isn't actually scoring that poorly.

Where are you getting those percentages?

I'm not sure what your database is like, but by using Bigbase 2006 (updated with TWIC every week) Black appears fine.
Not as good as in the Nimzo, but certainly not 65%-70% for White in the standard lines.

After 1.d4 d5  2.c4 e6  3.Nc3 Ng6  4.Nf3 Be7  5.Bg5  (or whatever move order you like to reach here):

5...h6    gives White 54%  (a.k.a. 'standard').

In particular, the Tartakower scores better than standard (as you mentioned), but even the much maligned Lasker's yields only 57% which is far far away from 65-70%.   

The Orthodox/Capablanca lines (i.e. lines with ...Nbd7 and no ...h6) all yield around 60% historically.

During the past 5 years the number of draws is increasing and white wins are down 
From the usual 5.Bg5, I show White scoring 59% (and after 5...h6 white scores 57%).
5.Bf4 scores a hefty 65% ... however, after a quick ...c5 the percentages are all down under 60% 

The lines with Bxf6 are 55% historically but have been scoring better in the past few years (mostly due to rating discrepancy).
Alatorsev (3...Be7) is giving 58% in the past 5 years, etc. etc.

Anyway, I hope this helps.  Of course, never forget that statistics lie.

The truth is that the QGD is super solid, has a terrific pedigree, and is in no danger of giving up 65%-70% to White in its mainlines.
Don't believe the Hype.   
Now go play the Nimzo and enjoy nearly 51%.   

Cheers.

Yes I would imagine semi-slav Meran type positions have a larger percentage of wins and losses for Black, whereas classical QGD systems have a larger percentage of draws, but that is not to say they are boring! I used to think that for years, but look at the great World Championship  matches in this opening

statistics! Dont be fooled QGD is a great opening, scores great for Black if you play it properly!