Well.... yes and no. While it's true that when a theorem is proved for the very first time, it doesn't matter much how, it's also true that there is some ongoing interest in finding simpler and shorter proofs for complicated ones-to find a shorter and clearer route to the theorem, so to speak. This still can (and does) advance mathematics in some cases, and also, a more succinct proof is more satisfying.
In the case of Fermat, supposing the (extremely unlikely) event that an amateur today would suddenly come up with a correct proof that uses only basic mathematics and that fits on a single page (let's be generous here instead of only allowing a margin), I doubt the proof itself could advance mathematics very much by now, but I'm still convinced the mathematical world would take significant notice- if only to see which simple key ideas and in which connection were overlooked by all those professionals working on it over 4 centuries- and then if those key ideas could also be applied elsewhere.
