If you did this, there would be no point of having bounties - because every user would start a bounty on their questions.
The 'featured' list would be extremely full - your attempt to get more attention would probably backfire because nobody will see that question. So it would be harmful to encourage users to do something that isn't (and shouldn't) be possible.
The entire point of having bounties is that you give a bit of your rep for more attention, and to reward users for their answers.
Putting a small bounty on would tell potential answerers you don't really care about the question much - you can't 'afford' to start a slightly higher bounty to get a high quality answer. Personally, I wouldn't answer a question to get an extra 15 (?) rep - because the asker wouldn't think the answer is going to be worth a bit if rep. After all, rep is a bonus - it feels nice to get some rep.
Besides, what's the difference between 10 rep (for an answer upvote) and something less than 50 rep (the current minimum bounty amount)? Hardly anything. So I honestly don't think there's any point trying to encourage users.