One thing I’ve noticed lately is that you can fight zombies and run around looting and crafting things for weeks at a time (taking narcoleptic naps when exhausted enough), but you can still install three or four engines into a vehicle, read a book about advanced bionic devices and learn how to make them, craft ammo and improvised explosives, and generally be optimistic and effective regardless of when the last time you slept was.
I suggest that there be more penalties in regards to certain activities such as reading or crafting things, lower stats and speed and occasional naps don’t seem to be quite enough.
Things such as having the player function with a lower effective skill level, a morale penalty that increases up to a certain point once you’re exhausted, invalidating any crafting recipe that takes longer than a certain amount of time, or dramatically increase the chance of failing a crafting recipe (possibly due to taking a nap in the middle of it).
Something to make the player actually want (or need) to sleep before crafting a mutagenic serum they plan to inject themselves with, or craft home-made tactical nuclear weapons, etc.