Did Richard Teichmann fail to take his "bishop pair" idea to its logical conclusion? Playing Black in a game against J.R. Capablanca, Richard Teichmann accepted an isolated queen pawn as the price for getting a bishop pair 

On move 20, White played Nf5, attacking his black squared bishop on e7, which was protecting his pinned knight on f5. He accepted the exchange of the knight for his good bishop, then had to sacrifice the h pawn to free his king from the resulting pin.

[fen ""]
[Event "Berlin exh"]
[Site "Berlin"]
[Date "1913.11.20"]
[EventDate "?"]
[Round "2"]
[Result "1-0"]
[White "Jose Raul Capablanca"]
[Black "Richard Teichmann"]
[ECO "D63"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "75"]

1.d4 d5 2.Nf3 Nf6 3.c4 e6 4.Bg5 Be7 5.Nc3 Nbd7 6.e3 O-O 7.Rc1
b6 8.cxd5 exd5 9.Bb5 Bb7 10.O-O a6 11.Ba4 Rc8 12.Qe2 c5
13.dxc5 Nxc5 14.Rfd1 Nxa4 15.Nxa4 b5 16.Rxc8 Qxc8 17.Nc3 Qc4
18.Nd4 Qxe2 19.Ncxe2 Rc8 20.Nf5 Kf8 21.Nxe7 Kxe7 22.Nd4 g6
23.f3 h6 24.Bxh6 Nd7 25.h4 Nc5 26.Bf4 Ne6 27.Nxe6 Kxe6 28.Rd2
Rh8 29.Rc2 Rc8 30.Rxc8 Bxc8 31.Kf2 d4 32.exd4 Kd5 33.Ke3 Be6
34.Kd3 Kc6 35.a3 Bc4+ 36.Ke3 Be6 37.Bh6 Kd5 38.Bg7 1-0


Teichmann's alternative was to move the bishop back to f8, allowing White to take the knight (and double his pawns on the f file). In that case, he would have two bishops against two knights to compensate for his wrecked pawn structure.

Teichmann was down a clear pawn after the way he played, counting on bishops of opposite color to give him a draw. Would he have been at less of a disadvantage playing the way I outlined in the previous paragraph, given that two knights are worth less than two bishops?
I'm not going to claim in a black-and-white way that your idea of 20...Bf8 is strictly inferior to Teichmann's 20...Kf8 in objective terms, but I can think of two solid reasons not to play into the resulting 20...Bf8 21.Bxf6 gxf6:


Contrary to your general operating premise that two bishops are superior to two knights, in this position White's knights are fantastic, and in particular, Black's poor pawn structure is such that the knights have wonderful outposts to camp in, as well as weak pawns to target down the road. Really, I'd take either of these knights over either bishop in this situation, so much so that if I were playing Black from this point on, I think I'd feel compelled to trade one of the bishops for a knight at some point anyway, and so I'd rather have done so without having compromised my pawn structure in this way.
White's position in this line is much easier to play. White has no structural weaknesses, while Black has targets in her structure. The knights have natural squares screaming out for occupation, while the light-square bishop is especially hemmed in, not least because of the isolated d5 pawn.


It's tough to give detailed analysis of variations without inline commenting, so I'll just illustrate what I mean with a single line. After, say, 22.g4 to make luft for the king and grab space on the kingside, even a seemingly productive move like 22...Rc2?! for Black doesn't actually lead anywhere, basically because of the pluses indicated above. For instance, after 23.Ned4 Black can't follow up with 23...Rxb2?, because after 24.Rc1! White will gain a big edge while Black looks after her inferior pieces: e.g. 24...a5 (forced, as otherwise the b7 bishop will be embarrassed) 25.Rc7 Ba6 26.Ra7 Bc8 27.Rxa5 and White has a huge plus. Even if it doesn't look that way at first glance, if one plays around with this position a bit, it's much easier to find good moves for White, and it's actually quite difficult to bring the black pieces (including the king) into play without running into trouble.

[fen "2r3k1/1b2bppp/p4n2/1p1p1NB1/8/4P3/PP2NPPP/3R2K1 b - - 0 1"]

1...Bf8 2.Bxf6 gxf6 3.g4 Rc2?! 4.Ned4 Rxb2? 5.Rc1! a5 6.Rc7 Ba6 7.Ra7 Bc8 8.Rxa5


Again, that's just one illustrative line, and certainly one in which I picked a mistaken idea for Black for effect. But the point is, if Black can't effectively make an active threat like the one indicated without facing such a harsh backlash, then it's not a position in which Black has much of anything to play for, and instead is one through which Black must suffer and just hope to hold on. To me, that's reason enough not to go in for this option over 20...Kf8.