Could you run a local server on your desktop that you only turn on whenever as a client? I don't really understand the Fediverse's architecture yet, but as far as I saw instances being down are not a big problem beyond not being able to log in if it's your home instance, and communities fracturing to separate discussions in other instances' local federation caches that only get resynced when the thing comes back up.
What prevents me from running my own instance as a very heavy client? Discounting the public DNS + static globally routable IP part as those can be solved IMO.