I don't personally have an immediate need for this, but it seems like there must be those for whom it could be a life saver.
Allow bounties to be placed with shorter duration. Since the Featured page is sorted by date, this allows the question to jump higher on the list and gain more immediate exposure.
This does not increase the total exposure the question receives. Rather, it moves up the timetable of the question, giving it the exposure it already would get, but sooner. In fact, it reduces the total exposure.
This could be exceedingly useful for questions where OP has a deadline, and needs more immediate answers.
I can't think of any drawbacks to this, beyond the additional step of selecting from a dropdown (1-7 days, but default 7), and of course developer time to implement.