I believe the concern with putting target species, like say a salmon in a live well, is it opens the fisher to being suspected of High grading. And as i believe the rules state that any fish not being retained is to be immediately released in the least most harmful way. And the sea is certainly a better environment than a small fiberglass tank in our deck.
Having said that i believe commercial gillnetters have to have functioning revival tanks on deck to revive non retainable species prior to be put back in the sea. (so the seal don't get free meals) but that is not a high grading scenario as the fish in those tanks must eventually be thrown over board.