There's more than one way to address the problem of draw death besides bughousing captured pieces. Other win conditions are sometimes proposed - something like your king reaching the enemy king's starting square or back rank. Or count stalemate as either a win or some fraction between 0.5 and 1 for the side that inflicted it. Or do the same for draw by insufficient material (bishop or knight) for the superior side.

(I'm not advocating for any of these in particular. Although that's the problem - even if everyone agreed that we should add some kind of win or scoring condition, we'd never get a majority to agree on one solution.)