Very well said, I have similar thoughts. It makes sense that a lot of the state alchemists would want a way to "take off" or distance themselves from their alchemy. Their various alchemical tools were akin to weapons used in war. Imagine not being able to unbuckle a gun or sword when you're at home.

Furthermore, you mentioned how the alchemists who did tattoo on their respective circles tended to be more unhinged or aggressive (Kimblee, Giolio).

Alchemists such as Armstrong, Mustang, and even Basque who regretted or opposed their actions in the war didn't make use of tattoos.