There isn't anything new about this line. Petrosian was playing the black side in the 60's. Played a lot in Kasparov v Karpov matches by both sides. Sokolov explains in depth in "Winning Middle game structures" Short's approach with c6 and a5 seems to have most theoretical approval these days. 
              One of those lines were definitely prefer black side with two bishops, personally.

The Bf4 line is just stronger though...

GM Sadler: "The most visible drawback (to...b6) is that Black weakens his queenside light squares by abandoning his pawn protection of c6 and a6" (1). GM Taimanov remarks that this is why Black fianchettoes when the knight is still on b8. Also GM Sadler: "... it becomes harder to complete Black's development by connecting the rooks" (2). And "White's judgement is ... that the extra move ...b6 is more helpful to White than to his opponent."

One of the oldest attempts for White is 8.cxd5 Nxd5 9.Bxe7 Qxe7 10.Nxd5 exd5. Notice that White has helped Black to solve the second problem. It has been demonstrated that Black can solve the first problem too. This explains why White gives up the pair of bishops.
GM Sadler again: "We shall first examine the main line 8.Be2 Bb7 9.Bxf6 Bxf6 10.cxd5 exd5 11.b4. There are three intended consequences:

1. The passivity of Black's light squared bishop.
2. The weakening of Black's kingside light squares.
3. The deterrence of Black's freeing break ...c5."

Finally there is the matter of timing. The rule is to play Bxf6 áfter Black has played ...Bb7 as 8.Bxf6 Bxf6 9.cxd5 exd5 allows ...Be6. The bishop is better there because after ...c5 and ...c4 Black wants to support the queenside pawns with the rooks. Then Bb7 gets in the way. A sample line is 10.Be2 Be6 11.O-O c5 12.Qa4 Qd7.
After 11.b4 (from your original line) c5 12.bxc5 bxc5 13.Rb1 Black is on"the worse side of a draw"(IM Cox) and White is happy to exploit it. So 11.b4 c6 12.O-O a5 13.b5 c5 14.Ne5 and White hopes to prove an edge because of Black is a bit behind in development (Nb8. Ra8) and has potential weak pawns on b6, c5 and d5.

Whenever I think of the Tartakower I think of what Walter Mooij, a very strong Dutch corr. chessplayer once told me: after 1.d4 White can prove some advantage, but not a forced win. It seems to me that White should not complain after 7...b6 if he/she manages to do that.

I find the Tartakower defence annoying when I, as White, take immediately on d5 after ...b6. I see the latest from the top-GMs, with most success for White, is to play 8.Be2, and then, after Bb7, to take off the f6 knight with Bxf6, then to exchange the pawn, forcing the exchange of the Bishop or hemming it in somewhat. This is followed after the exchange with b4. So: 1. d4 d5 2. c4 e6 3.Nc3 Nf6 4. Bg5 Be7 5.e3 O-O 6.Nf3 h6 7.Bh4 b6 8.Be2 Bb7 9.Bxf6 Bxf6 10.cxd5 exd5 11.b4.... 

Should one voluntarily concede the Bishop pair to Black like this? Or, rather, can someone explain why this is favoured currently?