I see some rather interesting arguments here, specifically when applied to the high volume sites and most specifically Stack Overflow. Things move very fast here and when something falls off the front page, it could be lost forever. But at the same time, the smaller sites do not have this problem, so it seems that lifting the 2 day waiting period for those sites is unnecessary.
I think the best solution would be to consider a per-site configurable delay. You can leave it at 2-days for most sites, and then adjust it based on question volume for the high volume sites, but I would not go any lower than 6 hours. Anything less than 6 hours is just overkill, you'll end up with too many "instant bounties", most of which will be from help vampires and students with homework due in 3 hours. Plus, for reasons I'll go into next, the community needs time to appropriately handle the question.
Quicker bounties opens up another problem related to off-topic (and/or just plain bad) question with bounties (and the "URGENT HALP NEEDED" questions). It is tough to get a bad question closed in less than an hour at times, so you could end up with situations where a question picks up a few close votes very early then the bounty gets put on before the community can actually close it. Plus, I've seen references to users using a bounty to make their question close-proof* in some cases, and I think the usage of this method would increase. Someone sees their question has picked up a few close votes, so they'll throw a bounty on it to help keep their question open.
In order to make this workable, you would need to do at least 2 things:
- Prohibit early bounties on any question with at least one vote-to-close or flag-to-close. These questions can still be bountied after the normal 2 day wait
- Allow bountied questions to get closed without needing a moderator. Maybe allow higher rep users (10K) to remove & refund a bounty if a question has close votes.
*- We know it isn't really close proof, but it is harder to get a bounty question closed since you need to get a mod involved.