Okay, I may as well mention straight off that the main reason I am asking this question is due to the upcoming reputation recalc.
It has always seemed silly to me how bounties affect privileges. After all, if rep is, as oft repeated, primarily a way of how much the system trusts you, bounties really shouldn't affect that. In terms of effects, this would lessen the pain from the rep recalc. One downside - this increase the number of bounties given out as users wouldn't be saving up their rep to gain privileges, so maybe it would be sensible to enforce a minimum reputation (500?) before you can post bounties.
PS. If people are worried about others gaming the system, the better way would probably be to make the extra reputation gained from bounties not count towards privileges, rather than removing privileges for posting bounties.