Continuing the other topic…
The reason of why Synths cannot use armors and perks is because your own game says so.
I believe I saw this before talking about Trooper/Patroller, because they have pretty good armor, and they cannot wear “another” armor because it was said they have already an armor in their own character/unit card.
Edited: Personally, I think this could be redone in the future, at least for Gen 2 synths (Gen 3 have no Synth icon, so they could be equipped as normal), for being equipped with some armors/clothing/perks/heroic.
Edited 2: Long time ago, people asked why the Heavy Synth Armor could not be worn by any synth, because it seemed a bit incoherent.