The question of whether there is a missing finite simple group is a precise question. But what does it mean for a natural language proof to be valid? Typically a proof contains many precise lemmas and one could ask that these statements are correct (though this leaves the question of whether they prove the theorem), but lots of math papers contain lemmas that are false as stated, but where the paper would be considered salvageable if anyone noticed.

Similarly, the Riemann hypothesis is widely believed due to a combination of partial results (a positive fraction of zeros must be on the line, almost all zeros must be near the line, the first few billion zeros are on the line, a random model of the Mobius function implies RH, etc.)

This is a very standard list of evidence, but I am skeptical that it reflects how mathematicians judge the evidence. I think that of the items you mention, the random model is by far the most important. The study of small zeros is also relevant. But I don't think that the theorems about infinitely many zeros have much effect on the judgement.