I have a zombie spawner and I've built a farm around it. A lot of zombies drop down to be killed, but not a single one has dropped any armor/item. I've been killing them with a Looting III diamond sword. At this point, I've killed about twenty groups of zombies (with roughly 2-3 armored ones in each), and still nothing!
If the chance is 11.5% per armored zombie, then after about 40 armored zombies total, the probability of not getting a single piece of armor is (1 - 0.115)^40 ≈ 0.75%. Yet, I'm still trying while writing this text.
In other old (recently, but from a old version 2-3 months ago) games, armor drops are a problem because they occupy a lot of space and are basically junk, and they appear VERY frequently.
Most of the zombies I've killed for this test are from the spawner. I also tried naturally spawned zombies, though in too small a quantity. They drop the armor that's given to them but not the armor they generate with. I even tried in another world, without success. I also tried a different sword (a crafted iron sword, on printscreen), but nothing different comes out.
How to reproduce:
Open a world on 1.21.4
Search for armored zombies or look out for a zombie spawn
Kill them with any item or sword with looting III
Duplicate of MC-278683, which will be fixed in an upcoming release.