All the correspondence chess games (after 10...Nd7, one annotated) I could find:

Historical tidbit:  4. Qxd4 caused some consternation when Salov tried to play it against Ljubojevic in an Open Sicilian theme tournament (in honor of Polugaevsky) in the 1990s; he was told he had to play 4. Nxd4.

Some older lines of 4. Qxd4 also involve c4.  I suppose the OP knows about this being a Maroczy Bind structure ...

I think this belongs here, but I'm not sure, as I was told that after 3.d4 is not an anti-sicilian anymore.

As I wrote in the other forum, the vast majority of my games with both white and black are four knights; however, as a 1.e4 player, I do face the sicilian from time to time, and since I like the open positions but I'm totally horrified by heavy theory I followed Watson's advice in his e4 book and settled for the line mentioned in the subject, which gave me quite a few interesting games (all of which went Bb5, Bxc6, 0-0-0 and smooth development followed by a reasonably often successful attack on the kingside).

The thing is, taking a look at a database at the club (all the games played in the last year) I noticed that while white is currently scoring boatloads of points with this, the fashionable variations have become quite weird:

4...Nc6 5.Bb5 Bd7 6.Qe3!?
4...a6 5.h3!?

Usually playing c4 afterwards. While I don't like too much these kinds of middlegames, it is interesting how much popular (and successful) they are. And I was kind of amazed that  they are not covered really much here in the forums; actually, I don't think there was ever a book on this variation written from white's perspective.

So the question is, what's the (is there a) theoretical consensus on these lines? And why are these systems with c4 considered more effective? 

And a last thing, why is Qxd4 not that popular at the top level? c4 or not, the resulting positions don't look drawish at all, at least to me (well, maybe that's it ). Actually I much prefer to be white in these games than in the 4N, but while I see top players taking the white side of the 4N (Short, Giri), no one ever goes into 4.Qxd4. And I don't buy that's simply because Nxd4 is better (it is, right?), since in the open games you also have a theoretical better alternative in 3.Bb5. Maybe they just spent so much time searching for novelties in those Nxd4 games that they hope to use them?

PS Yes, they're GMs who studied chess for decades and I'm a chess-nobody who knows nothing; that's why I'm asking.