I've picked up Daedric and Dragon armor pieces at around level 55-57, random chest loot both times.
Level 36, legitimately just found Dragonplate Gauntlets inside of a master-level chest.
That seems hella low for Dragon gear.

It might be that odds are just extremely low in the middle levels compared to higher levels of your character.
For example, maybe a piece of Dragonplate has like a 0.1% chance of spawning in a chest at level 35, but the odds of same armor spawning at 55 are 1-2%.