First of all let me mention that I have thoroughly researched meta on topics regarding the awarding of bounty to the asker, but every time it was about a mistake made, or no answers posted, etc...
I know that bounty does not ever get returned because of mere fact that it draws attention to a question and people put time in trying to find an answer. It should not be free.
But now, I've had a question on SuperUser to which, 1 day after I've issued a bounty, I found the answer by pure coincidence.
Now, does it not seem fair that I get the bounty at the end of the period, if no better answer is provided?
There is no gaming the system in this case, there are the upvotes on my answer to prove that.
Another point that imo is fair: The bounty does indeed draw attention to the question that I should not get for free, but my answer may help people with the same problem. Perhaps the bounty makes them stumble upon that question, they read it realising they have the same problem, and they read my answer which helps them as well.
Now let my point be clear, I have absolute understanding why the system is so strict about not giving back bounties, because among privileges they are the reason why reputation exist. Please see my question on SU meta that also regards the bounty system: Do not take away earned privileges. Tom Wijsman makes some excellent points in his answer.
However, I would like to open discussion about permitting one exception to the rule of never giving bounties to a self-answer. The condition is that a self-answer needs to have the highest amount of upvotes, and maybe along other conditions (like "surpass the second-best answer with a certain amount of upvotes", or "the question needs to have a number of other answers as well"), this exception is justifiable.