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).

so I can stop paying those home internet connection bills that keep stacking up every month?

If you personally don't want to have an internet connection then I'm afraid it's going to be hard for you to run a webserver for free. I think this would be unusual though.

the point is that http isn't free of ongoing costs.

Are you paying for http on top of your internet connection costs?

Or I might get free access from my library and they don't permit me to run a web-server.

I'd probably get a more expensive plan that had good upload speeds.