What happens to those questions which had a bounty and whose answers are accepted by the OP? Where do they go? Unless I favorite all such questions, I would have no way of seeing "previously bountied questions" which have been "answered". Having such questions marked specially would be a great asset because bounty questions are no ordinary questions, they are one step (or more steps) beyond ordinary.
Having such questions marked specially would be a great asset because bounty questions are no ordinary questions
I have no idea why that would be true; normally bounties are on questions that haven't gotten a satisfactory answer. Either that's because they're really hard, really obscure, or because they were confusing/poorly written and nobody wanted to bother, but the OP put a bounty on it because they were desperate.
In any case, you can use SEDE to list all posts that have had a bounty: https://data.stackexchange.com/stackoverflow/s/1508/all-bounties