This one’s easy. You need to get resources to maintain your stuff. The places near you have either have already been looted by you or someone else, or are too dangerous/hard to get to for looting. It’s easier to drive a few hours to a new city for new resources than delve deep into a zombie horde infested nearby city center.
Exploration is desirable because it’s a necessity to maintain your tools and weapons.
I think there’s a lot of potential there. I think maybe we could also have some stuff that you have to find that you can’t make. Maybe 1 or 2 in each large city, or rare parts that you need to be able to construct things at your home base?
If you’re going to force players to scavenge for maintenance resources there should be cues leading to them. Take the atomic reading lamp as an example: as far as I know, you can very rarely find them by searching hundreds of homes, which is OK for a curiosity item, but really annoying if it is something you have to find with some regularity.
On the other hand, oxy torches can rarely be found in homes, but fairly reliably be found in garages, and I’d find it fairly reasonable to locate such a facility (which isn’t very rare), plow a path through the hordes, and search the facilities with a good chance of finding what you’re looking for. However, if the game is geared towards renewing some kinds of resources, it should also provide hints as to where those resources can be found, if it’s not self evident, rather than having players stumble around and gradually figure out where you’d find different things that aren’t placed according to any visible real world logic (or according to a real world logic that can’t be expected to be common knowledge for the player base).