The Dursleys never cared enough to invest that much effort in Harry's wellbeing. I'm pretty sure the only reason they got him glasses because (in the US at least) they test your vision in school. Then when he was older he was less involved in the Muggle world and less inclined to seek out Muggle solutions/products. Though this brings up another question: why isn't there a vision correction spell?

Really, though, can you imagine Harry without his glasses? Thought not. XD

Or maybe because he doesn't like the idea of touching his eyes regularly enough to use contacts. I know a few people (myself included) who couldn't use contacts if required for this reason.