As far as the best people not running for office, we ourselves are to blame. When we insist on knowing every teensy little mistale a candidate has ever made, and insist on that record being more perfect than any "normal" person, we are chasing most of the good candidates away.
As an example, I have always wanted to be a local city councilman. Almost everyone who knows me or has met me has urged me to run. I thin k I'd be very effective at the job. BUT -- way back, in my distant past, I had a run of bad luck, some bad judgement, and I had some bad debts. If I ran, someone woul discover that and hold it against me. I haven't made any debilitating mistakes for 35 years, but those past mistakes would be thrown in my face., I don't want it, I don't need it, and the best way to let those sleeping dogs lie is not to run for office.
Some may blame the media for this. In most cases, probably including mine, it's only the media who has the resources to make these kinds of investigations. But, the truth is, the media wouldn't do it if their readers and listeners didn't demand it. The media is, after all, a business, and they won't continue to produce a product no one wants.
So, we, ourselves, are to blame for smart, savvy, essentially good people not running if they have ever made even a minor mistake.
The idea of a draft for President would not work for the same reason. As soon as Joe Blow was drafted for the office, every pore and sweat gland would be opened for the public. I don't know of very many perfectly clean and innocent individuals out there; I suspect most of you would run for Mexico or commit suicide rather than go through the gauntlet of being drafted into a public position. Remember, if they can't find anything else, they'll throw your speeding ticket at you, or find that picture of you at a party.
This was always bad, but never as bad as it has been since Ken Starr. Yes, Clinton tried to bluff his way out of his "problem", but that "problem" would not have been an issue with any other President until then. Certainly, no one would have been paying people to tape record other people's conversations...oh, wait. I forgot about Nixon and the Watergate breakins; yes, there is a history of certain parties pulling absolutely rotten stunts.