commie
I don't think that DS is about managing your resources until you can frag the local zombie population.
The point of a zombie infestation is to hostilize the environment around the characters, not to kill them outright. You want said characters to scramble for a defensible position and fortify it, because just standing around or moving out in the open is dangerous (it attracts more zombies, of which we assume there's an infinite amount of). The beauty of such a configuration is that, when you lock up people in a certain place and siege them, their resources will be consumed at a determined rate.
Eventually, and this is (IMO) the real objective DS is aiming for, the situation evolves into a) efforts being made towards acquiring more resources, with all the dangers and misadventures such would entail, and b) straining of group dynamics as roles are defined, priorities need to be established and morale needs to be maintained - the problem is, everyone has their own conception on how exactly all these things should work (the guy who thinks his decisions would do better for the overall group, the person that thinks survivors should be turned away because resources are scarce, the one who thinks the other isn't pulling their weight, and so on and so on).
I'm reminded of the Night of the Living Dead movie, with the characters (a ton of survivors of all kinds, which make for numerous points of conflict) cooped up inside this random country house. The place is fortified, they're safe inside, but for a certain reason they decide that someone needs to man the truck outside, fill it with gas and drive off. Of course, they're surrounded by zombies. That's when the main character remarks something like "they're so slow, we can easily outmaneuver them", which is totally true, and they make it to the truck without a hitch. Of course, the situation goes downhill as things don't work out as they were supposed to, someone dies, survivors retreat back to the house, and eventually people start shooting each other.
TL;DR - The zombies are the catalyst that allows for tense situations to happen and not necessarily the big bad monster you're supposed to be focusing on.