It strikes me as odd, but I suspect that most D&D characters are technically homeless.
This varies for other RPGs, of course. Many PCs in modern games have homes.
Having a home in an RPG is often something of a liability. In a Mage game I played once, I sunk a ton of background points into a mansion. My PC had Resources 5 and both Node and Library (and maybe Sanctum… it was a long time ago). The first session began with vampires trying to steal Tass from the Node in my basement. In fact, I believe that nearly every time that mansion had screen time, it was being assaulted by either vampires (usually) or the Technocracy. Unfair? Possibly. Annoying? Yes.
On the other hand, in the Mage game I’m playing in currently, the group has a shared base of operations that was designed by the GM… and he more-or-less made it unassailable. Different GMing styles? A proprietary feeling toward something you designed rather than something your player made up? I don’t know.
Personally, I prefer to run games with home bases. I think this is why I’d prefer to run an urban D&D game to a wilderness-based one. With a home base, you can easily get recurring NPCs with whom you can develop relationships. You have a place where other NPCs can go to contact the PCs specifically. You have something that you know the PCs will care about.( The trick is to not continuously threaten its existence.) You have a central site where people can join and leave the party (if you have players that miss games). It strikes me as more efficient from a GMing perspective.