In his Indiscrete Thoughts Gian-Carlo Rota writes:

Every mathematical theorem is eventually proved trivial. The mathematician's ideal of truth is triviality, and the community of mathematicians will not cease its beaver-like work on a newly discovered result until it has shown to everyone's satisfaction that all difficulties in the early proofs were spurious, and only an analytic triviality is to be found at the end of the road.

According to Rota what you ask for is the normal case. He - and others - do not even rule out the possibility that some day Fermat's Last Theorem turns out to be "trivial".