I think there might be fewer people who actively seek them out, so competition might be similar to any other job. I know a common sentiment I see spread around to would-be remote workers is that you need to work on-site for a while and then be given the chance, which isn't always the case.

This is just me speculating though. I had no issues finding a fulltime remote gig but I think it might be more common for people like me in the DevOps/cloud area than strict developers maybe.