+1 I like the reasoning behind the idea. If SO cares about the vast number of unanswered questions, something definitely needs to be done in that department. I think there may be too many practical problems though.
Many unanswered questions are abandoned, i.e. the user who asked them is not likely to return to SO. You would have to introduce community question closing at the same time for this to have any effect - I'm not saying I'm totally against that, but it would be a major change to the system with a plethora of issues.
Also, a bounty would put considerable pressure to close the question. A time limit to decide who gets the bounty would be necessary to avoid disappointment among people putting energy into answering the question. On the other hand, there may still not be a right answer, simply because the question is so hard, nobody understands it, or it's badly worded. What do you do then? In a normal bounty, there's the 7 day time frame after which you have to make a decision. What kind of time frame can you enforce on a year-old question? What if the user logs on to SO once a year? And so on an on. It's going to be too difficult to implement, I think.