[m00n]

To take one of your examples that I happen to be familiar with: Wiles' proof of FLT. I can assure you that in the >20 years that this proof has been out, thousands of professors, postdocs and grad students have read and reread every line of the two Annals papers.

They have been the foundation of hundreds of Phd projects and the scientific merit and public fame to be gained by finding a gap in the argument is clear.

Actually I think breakthrough papers are least problematic when it comes to unverified claims in math.