Say I post a question that I am looking for a solution for and one or two people answer but they do not provide enough information OR provide only partial info that does not lead to the answer, I can then put a bounty out in order to try and get an answer from the community. However, if during the bounty period, I ALSO research the question further and find a solution and I post the solution as the answer, SURELY I deserver to get the bounty returned or at least half returned right? Would you agree that this is a fairer system than the current system?
This was (kinda) possible at one point now long in the past - it ended up just being abused, and tended to result in bad blood between answerers even when used properly.
As Sdry notes, the bounty system was intended to provide a way for folks to attract more attention to questions they felt needed it; it's not a way to "pay" for answers. You can offer a bounty and get no responses, offer a bounty and solve your own problem, even offer a bounty and not get an answer until after it's expired.... In no case will it be refunded. In exchange for the reputation you give up, the post is highlighted for a period of time - whether you get anything else is up to the folks viewing it.