The Cloudflare dependency is for networking, not hosting. It would be very impressive to see a self-hosted service available over the internet without introducing a 3rd-party dependency or two.
Yes, but my point is that there are many web hosting services, but only very few such proxy services to my knowledge. (Tailscale is another great option if you don't need public reachability.)
I don't think it's a great tradeoff, when optimizing for independence of specialized solutions at least.