I'm not completely dumb when it comes to positional play but I never understood what I would get in return for, say, Bd3 Bxd3 in the Caro Kann (e.g. Tal Variation). Or Bd6 Bxd6 in the London. (In the latter case, I could say "one less piece about to sacrifice itself somewhere in my castling position", but the former?)
The short answer might be "A statically bad bishop can still be good dynamically", but please, no stock phrases :-) So what is the exact reason (in the Caro Kann)?
Related but unrelated (I see no tactical reasons concerning the Caro Kann, at least no immediate)
Related but unrelated (So, there they play Be2. Chess is so illogical... :-)