I thought of the Jacobson density theorem in ring theory. At least for someone who does not do ring theory day for day, the way it is usually stated provokes a feeling of "M-mh. So what?" to which the ring theorist might reply that it implies the Artin-Wedderburn theorem and a (maybe unexpected) description of primitive rings. Whether its proofs are "technically challenging" is a matter of perspective; although the proofs I know are kind of easy to follow, I would not think that I could have come up with one (or with the theorem's statement, for that matter).