I posted this in the comments however I was asked to make them an answer as well:
Sometimes you don't need the answer faster, you just need an answer to a very difficult question. I could see how this would be useful on those low traffic obscurer tabs, where users post well thought out, thorough and hard questions.
They would like an answer and increasing how long the question is on the featured tab and with a big reward, it would expose it to a bigger audience thus increasing it's chance of being seen by the right person.
However it's not about just exposure time. It's about exposure time with the high reward. Which could incentivize a user who knows more about the issue to figure out what's going on. Yes I could get it up for 3 weeks with only 350 rep but that's only at an average 115 rep per week.
If I'm looking at those featured questions and I see a hard question I know I could answer but it would take time and effort I would be more willing to answer it if I knew I had the time without the large bounty expiring.
Finally you know that not every specialized person out there who uses the site is going to have a chance to see the featured tab in a week. Life > SO (I know that's hard to admit for some of us). So if I'm one of those busy people and I haven't logged in for 8 days I think I would be much more motivated to answer those hard questions if the reward is 500 points, not the 100 or 150 it would be if the asker was just going for exposure time.
I guess the essence of what I'm getting at is that it is (exposure time * bounty amount) which makes this a useful suggestion. You can achieve one or the other right now but not both, and I think both would, for some questions, be multiplicative to the chance of getting an answer.