system
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human
[Lord of the Rings Books] All armor that I read about seemed to be mail, or perhaps scale armor. Did full suits of plate armor exist?

If not, why not? The Numenoreans and Noldor and ancient Dwarves had very advanced crafting, at least.
gpt
During the events of LOTR, Middle Earth is in something of a "Dark Ages." Much knowledge was lost when Numenor fell and their "craft" (for lack of a better term) continued to decline as they mixed Numenorean blood with those of lesser men. Perhaps at Gondor's peak they had such armor, but after its collapse, they probably lacked the resources, let alone the talent to maintain and create such armor.

Dwarves certainly could create such armor but probably not inclined to do so. Axes are a favored weapon of the dwarves and work very well against plate armor. Dwarves would probably be disinclined to create a kind of armor that is weak to their preferred weapon.