The OP is may not be an expert (tons of questions are asked by first time users). So we are putting the first answer that appears in the hands of someone who probably doesn't care all too much.
That's a very compelling argument, in the way that you put it. Questions are often asked from limited perspectives, and sometimes a user doesn't even know just how useful the feedback received is. and Pekka makes a good point when he said:
There's nothing more embarrassing for the site than an incorrect accepted answer. There's plenty of those, and the general consensus is the check mark isn't that important. Why should it make a difference in the sort order then?
Also, Bill-the-Lizard points to a useful query hereBill-the-Lizard points to a useful query here showing many questions that are accepted but have a negative score
Also, On very popular questions, currently it's sometimes a bit of hassle to scroll down to the find the best answer if it isn't the chosen answer.