While there are without doubt a times when the chips are down the rounds are coming back at you where you want if not need body armor. But, the question is when fighting the undead, do you really need body armor? Or are you better off using the weight for other equipment.
Modern body armor is designed to stop a wide range of projectiles, from the low end Level II vest and general pistol rounds too Level IV vest with hard ballistic plates and even vests designed to hinder the lowly Taser. However, modern body armor is not designed to fight the undead, at least not in original design. It is also, and most importantly heavy.
The weight of modern body armor, is substantial. Low level vests can weigh as little as ten pounds while the top of the line military issue OVTs can weigh thirty pounds or more. With the ZAC standard rifle being the AR-15 each pound of weight that you carry means one less magazine you could be carrying instead, or extra food, commo equipment, or any number of other gear.
While those who are dealing with pocket of human resistance or positions where they may be taking fire from others may have a need for a ballistic vest, those fighting solely the undead do not have to, in most circumstances, worry about the undead shooting back. If the undead are not shooting back would that weight not be used better in carrying more ammo, gear, or just plainly lightening the load on the lowly grunt who is pulling the trigger against the undead.
Another consideration is that those wearing body armor who have turned may also pose a risk against the living, since if they turned in full body armor, helmet and all, it would mean that there would be the need to place a kill shot in a tight area as well as making it harder to kill them with non-firearm weapons. On the plus side though a zombie in full body would also be slower. Then again so would you in full kit.
The general seed that I am attempting to put forth is that you will need to be cognizant for the situation that you will be entering and preparing accordingly. However, when fighting the undead, toe to toe, gun to flesh, and machete to skull, full body armor is not a required. If the situation is uncertain perhaps a compromise would best serve you, perhaps a plate carrying Level IV standalone plates.