Anyone who isn't comfortable with that is more than welcome to keep their privacy and not get on the ballot. If you don't want to fill out an SF86 then you don't get to work in a job that requires a security clearance. That obviously stays private but since the public is the one doing the hiring in this case, the public deserves information to make an informed decision.
With the caveat that the minimal constitutional requirements are the law of the land, the above is an example that makes an interesting debate topic.
Do I want a President that can't get past the same SF-86 process that I went through? The same might go for a drug addiction. A non-FOIAble process (SF-86s are currently exempt from FOIA, other than in a redacted format, AFAIK) to "apply" as it were, would likely eliminate a good number of presidential candidates. Would Kennedy have been President? Nixon? Clinton? Obama? Trump?
Though the negative part is that a portion of the SF-86 process relies on an investigator. What if the investigator's name is Peter Strzok?
Also, of the names I listed above, a large portion of the US population, at one time or another, considered them good presidents and were happy that they were elected, even if they couldn't have made it through the SF-86 process.
Which kind of leads us back to "minimal requirements". Otherwise we go to what we joke around about here once in a while - a comprehensive IQ test for every US citizen over 35, and whoever gets the highest score is dragged out of their home kicking and screaming and forced to be President.