Why do such a small percentage of people award 'best answer' to their questions?

No one really knows for sure. Yet Most 'seasoned' users like yourself will say that the majority of questions are Never returned to by the OP. It seems a great Many of them get their answer ( especially homework ) and then leave. In the days when we could delete our Q's, Many would do that instead. It's likely the reason why Yahoo disabled that feature - possibly hoping the OP would choose at some point.
Regardless of the reason though - with YA's 'bright idea' of opening All resolved Q's it seems a bit unproductive to choose a BA. Even if you do find 1 to answer the question at hand - hundreds of other users ( Mostly point gamers/spammers ) get free roam to lay down their thoughts. This has made a lot of users abandon the question even more than they did before the change.
So until YA limits the Q's asked to BA's chosen ratio - the percentage will likely decrease even more, especially on our own BA percentage.

Many are new and have no idea of what best answer is. Many times I will just see an additional answer saying thanks and that is it. Some people think thumbs up is a vote. Sometimes there is no best answer. I will not pick the best of the worst. I will wait until I get a good answer even if it takes months.

People either don't know how to choose a best answer or don't know they can.