It was an application from Cornish people who for a long time have felt their identity neglected, more to do with emotion than politics. The Welsh and Scottish have successfully done it as well. If you felt deeply about being Cornish wouldn't you support the idea? The fact that the EU is a ridiculous institution is not a reflection on the Cornish.
like much of Britain, people have moved around, a lot of people who reside in Cornwall are not native born and bred Cornish. Many left after the industries they once worked in slowed down then stopped.
i have spent a fair bit of time in Cornwall, most of those i met were blow ins - those born in Cornwall, and can trace their family history are getting less and less, as the work dried up, though fishing is still a staple, tourism is their biggest asset.