This is an old issue, but it still annoys me.
The number of points is a good estimate of how trustworthy a user is, and how much a user cares about the community. With that in mind, the argument that someone will start a bounty question and then never come back, is kind of moot. You need a good deal of reputation to start a decent bounty. In that regard, those who start bounty questions have already proven themselves trustworthy by gaining the points they use for their bounty.
So what's my point with this? It's that I trust a bounty-questioner more to give a user his bounty and accepting the answer if he/she deserves it, compared to a gazillion users who can give useless and/or irrelevant answers just to get the auto-bounty. People don't show much restraint.
That people can give plain wrong answers and get the bounty is not a very good intensive for starting bounty questions. And that the system automatically picks an answer as accepted and 'correct' when there is no such thing is just adding insult to injury.
The least one could do, is what Ngu Soon Hui and time suggested. Leave the 'accepted answer' up to the user who started the bounty to decide. If the system picks automatically, it is not because the user is absent or left SO, but because there indeed was no right or helpful answer.
The solution is: If there is no accepted answer after the time limit, give the points to the answer with the most points, and degrade the bounty question to a normal question again, but do not set the accepted answer. Then one can start a new bounty again, or leave the question as a normal question for a while.
Right now, the system is an insult for the people who spend their points on this, and for others who search up the question and find wrongfully accepted answers, it's shear misleading.
P.S I have a difficult question I planned to add a 2000 bounty on, but I probably just spend a 1/10 of that amount now, since I most probably won't get my points worth. If you consider the bounties on most questions, it seems I'm not alone. Most bounties are on around the 200 mark, with 50 of the points added in.