Agreed that it's not crazy at all. And I certainly wouldn't propose taking a pay cut. Assuming you can actually stay on task and produce quality work remotely, you will actually cost the company less than if you were in the office. (They don't need to supply you a permanent desk, etc.) What you should prepare to do though, is make it easy for them. Have solutions in mind for all the standard issues. Are you willing to commute in for all meetings? If not (and it would be a waste IMO), set up and demonstrate a working videoconferencing solution before you leave. Perhaps suggest quick daily check-in emails, to keep your team up to speed with what you're doing. Etc. Basically the only challenge isn't to get your employer to accept the idea; you also want them not to regret it afterward.

(Everyone at my (very small) company works remotely. I love it, but it does come with its own unique challenges. As nl mentioned, they are likely magnified if you're the only remote worker.)