This is a rather interesting thread you've got going. My 2 cents from a philosophical perspective...
Certainly you'd all agree that there were certain standards for entrance to your undergraduate institutions? There were some people who applied and did not get in after all, no?
With each successive step in your education, the standards increase--for example, when you move from 1st grade to 2nd your teachers don't expect less, they expect more. Given "some reading ability" as a criteria to progress, it is ridiculous to think that just because a 1st grader *really really really* wants to read that they should progress to 2nd if they still can't. I would doubt it would be a good idea to just "give the kid a chance" if they have not been successful up until this point. (An aside, this seems to be what has happened when we graduate high school seniors who can't even read--we give too many "chances" without seeing results!)
There is another faulty line of reasoning: that you can be anything you want to be only if you try hard enough. Now, there are occasions where someone's hard work pays off in such a way that they become something they might not have had they not given it the effort, but that is different. I could not become an opera singer no matter how I tried! Why? Not because of lack of desire, because I would really love to be able to sing well... It's because I simply have not been given that gift. I could certainly take voice lessons and give it my best shot, but at some point along the way someone would have to say, "your gifts lie elsewhere." There would be some criteria for making this 'judgement' of my ability--my voice is weak, my range is small, I have no power... Try as I may, I can't force myself to be something for which I am not naturally inclined--and my performance in a variety of areas shows that. Opera needs to have its standards too--otherwise it would turn into a karaoke night and it would no longer be opera. (Either I have to puff up my abilities--pretending to be something I am not--or I have to lower the standards--these seem to be the options)
Likewise, medicine needs to have standards to even call itself medicine--it needs to have people with keen minds with abilities well beyond average, they need people who have caring hearts and service oriented sensibilities. But you can't have just some of those qualities and not others.
(Another aside, I tend to think that many of the prima donnas in the profession with bedside manners from *hell* probably shouldn't have made it into medical school either--by allowing such people to practice medicine you do accept such behavior--ie, lower the standard for what it means to be a healthcare provider.)
Progressively, you are weeded out by successive levels of education so that the cream rises to the top, so to speak--until finally, when you reach the level of applying to medical school, you undergo a further weeding.
I think, in concept, that having GPA, MCAT scores, letters of recommendation, and an interview all as criteria to move to the next level, will provide a vast breadth of information about someone such that you would get a pretty good picture of who they are and what their abilities are. If you perchance performed weakly in one particular area in a way that doesn't describe your gifts accurately, chances are that the other criteria they look at will show a disparity. Or, you will improve yourself in that area by trying again and doing better.
Certainly, improving your score in one area doesn't change who you are--it proves who you are and the potential you have.
Perhaps if you were the head of the AMA or AOA you could change this procedure, but I'm guessing that they wouldn't give you that position either just because you "thought you could be good at it."