Yes, you can host your own server and use your home internet connection. This is the whole issue really - the web was designed as a decentralized, anarchistic, read/write thing, and it's subsequently become a thing where it's increasingly difficult to participate unless you're doing so on a professional basis or relying on somebody else's professional services. Maybe this is just how it has to be, but for people who can remember a couple of decades back it's pretty depressing.

(btw I've used LE both in my day jobs and for some personal stuff, and I very much appreciate its existence).