This Datapack stops entities from dropping their armor when they die. The best part is that if a zombie picks up your armor or other items, it'll still drop them when it gets killed!
Special Thx to u/GalSergey for showing how to do this in a command on Reddit to some guy 4 years ago. 
Only tested on 1.20.1. It MIGHT work on other versions
It works by automatically setting the entities' "HandDropChances" and "ArmorDropChances" to 0.0. The entities are also given the "NoDrops" tag, so the "command" only gets run once per mob
The command:
Spoiler
You can easily edit the command by extracting the zip file and editing the following code to add exceptions or only make it work on specific mobs
execute as @e[type=!minecraft:player,tag=!NoDrops, type=!minecraft:item, type=!minecraft:experience_orb, type=!minecraft:end_crystal, type=!minecraft:ender_dragon, type=!#minecraft:boat] run data merge entity @s {HandDropChances:[0.0f,0.0f],ArmorDropChances:[0.0f,0.0f,0.0f,0.0f],Tags:["NoDrops"]}
