We actually intentionally don’t make criminal convictions a barrier to the Presidency because a corrupt government could just disqualify a political rival by securing a conviction in a kangaroo court on trumped-up charges. I think it’s a good thing, but like most of our government it only works with an educated voting population, which we lack.

There’s rather a lot of undesirable traits in a candidate where the mechanism for blocking them from winning the presidency is people not voting for them.