What, then, after he takes the bishop? I can imagine Capablanca rolling in his grave right now.
Black will be down a pawn whereas white will keep pressure on the a6-c8 diagonal. White doesn't need to get greedy and take the a7 pawn after ...Nb8 (but he can if the knight just sits unprotected on d7).
After the bishop exchange, black's center is distended. He can't cause white to surrender the center because of the queen's pressure in that diagonal. Black is better off finding something else to do with his time.
Lastly, to paraphrase IM Jeremy Silman's thoughts on a similar problem (Re-assess your chess, 3rd edition, pp. 106):
[Black would] have sacrificed the exchange. True, White enjoys an extra exchange. However, Black possesses an attack on White's weak kingside, enjoys an enemy king that is stuck in the center in the midgame of an open game (i.e., in front of semi-open files), and a bishop which assists with threats on the h1-a8 diagonal. In this way Black has several favorable imbalances to play with.
"Whether this would have offset White's material advantage is a moot point - never leave yourself with no favorable imbalances or no chances to create them."
If you do, you will surely [logically, because of no available counter-play] lose.
Another quote on imbalances by the same author, same book pp. 225 (sorry, but I really have to drive the point home here)
"Though we all can sacrifice material if we see a forced mate, many of us are less likely to part with our men if the return is just 'positional'. However, I must once again remind the student that material is just an imbalance like pawn structure, space, and all the others. Does it make sense to create one imbalance in your favor (material) while giving the opponent several others (space, better minor pieces, superior pawn structure, initiative, etc.)? Simple math gives us a clear answer.)
You can actually see what Capablanca had to say about the game (due to the centralized king in an open midgame, Black's rooks taking control of the d- and e- files, weakened pawn protection for the king, yada yada)
The play here was extremely difficult. I probably did not find the best system of defense. I can not yet tell which was the best defense here, but it is my believe that with the best play White should win.