It would increase the branching a bit but not much I think.
Taking your own pieces would be sub-optimal choice in every-case other then avoiding mate (at cost of your material), when sacrifice would lead to mating of your opponent.
Gaining positional advantage at cost of anything other than pawn is probably not worth it. AFAIK in high level play gambits are not true gambits as you get the sacrifice back.
Gaining positional advantage at cost of anything other than pawn is probably not worth it. AFAIK in high level play gambits are not true gambits as you get the sacrifice back.