The rationale of the 2 days delay before a new question becomes bountiable is that the community requires time to close a not eligible question.
The problem is with it, that the worth of an answer typically decreases a lot, if the bounty appears so much later. The motive to sacrifice a lot of reputation is much more weak, if the results arrive 2-9 days later.
My idea is that the OPs could have a possibility to ask for a community review of their question now.
I think it could be done most effectively in the close/reopen queue:
- The "start a bounty" link would be visible for the OP on the spot after he asked the question.
- If he clicks "start a bounty" before the 2 day limit, the bounty wouldn't be started. Instead, a close review would be started for his question (but no close vote entity would be created).
- If the question wins the vote (= 3 "leave open" votes are collected), then it would become bounty-able on the spot.
- If the question loses the vote (= 5 "close" votes), it would become closed as usual.
I expect the following results:
- There will be a little bit more close votes.
- There will be much more bounties.
- There will be much more users working hardly, but this time not for privileges, but to collect reputation for bounties.
- There will be less workload on moderators as they wouldn't need to cancel bounties as often, as the questions will be reviewed.
In general, the sites would switch from the current "work for privileges" and "google for knowledge" flavor to "knowledge sharing" direction.