My guess is that with this kind of material imbalance, the two central pawns are worth more than the Bishop.

White, who won't be materially inferior, would get all of the initiative in the center, and black's king won't find safety anywhere.

Here is what Stockfish has to say in regards to it,

Position after 13...d4

click for larger view

<14. Bxd4>

[14. Nxd4 exd4 15. Bxd4 Bd6 16. g3 O-O 17. Bxf6 Nxf6 18. Be2 (18. e5 Nd5 19. Rxd5 Bxd5 20. exd6 Qxd6 +0.64 at a depth of 17) 18...h4 19. Rxd6 Qxd6 20. e5 Qd5 21. exf6 +0.88 at a depth of 27]

<14...exd4 15. Nxd4 Qb8 16. Nxe6 fxe6 17. Bc4 Qc7 18. Bxe6 Qxc3 19. bxc3 Nc5 20. Bh3 Na4 21. e5 Nxc3 22. exf6 Ba3+ 23. Kd2 Nxd1 24. fxg7 Bb4+ 25. Kc1 Rg8 26. Rxd1 Rxg7 27. Rd5 h4 28. Kb2 Ke7 29. Kb3 Bd6> +1.81 at a depth of 27

Many thanks for taking the time to go into this!

I have a little confession to make though -

I didn't look at the long variation... it just makes me tired :-]

in such positions there are so many ways the game can develop, endings, attacks, blockades, sacrifices...

for many of the moves in these variations there are 4-5 alternatives which are within 10 centipawns of the evaluation. When you give 30 plies, this gives something like 10 to the 15th or 20th power possibilities for the game to develop, just for 15 more moves.

It's nice to see that the computer sees it as "0.64" or "0.88".

How many opportunities are there to go wrong?

How many times one needs to find a horribly difficult to see 'only' resource, 6 moves deep in the position?

A computer's 'verdict' doesn't increase our understanding of the game - although it does look mighty impressive!

You don't speak for me on this matter, so the inclusion of 'our' in your above statement is objectively untrue.