Whether there is an existing and verified proof or not, there is still a great mystery to be solved by figuring out what Fermat actually meant by what he thought as an elegant solution, whether it is an actual solution or not.

Well, it could have been like Kempe's chains... they finally realized there is a problem, and then it took like 100 years before Appel and Haken made what is probably the first computer-aided proof. And who can say it's really a "proof" if it doesn't explain "why" it's true.

Phrased in a way that doesn't imply Wiles's extreme longevity: it took 385 years of advances in mathematics to invent the tools and frameworks that allowed Wiles to come up with the proof.