I feel that in many lines starting with d4, such as the Queen's Gambit Declined, or especially the Nimzo-Indian, Black is more than happy to trade her King's Bishop for White's knight on c3. For instance, one frequent line in the Nimzo-Indian (reached in 3200 games of the chess365 database) would be the following:
[FEN ""] 1. d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. a3 Bxc3+ 5. bxc3
What strategic benefit does this hold for Black? She has given up the bishop pair, given White the chance to capture toward the centre with her b-pawn, in turn strengthening the d4 square for White, and moved the same piece twice in the opening. And yet, this seems to be a line where Black enjoys a higher win percentage than White, which puzzles me as it contradicts my naive understanding of opening principles.