That's pretty much how I feel about so much different types. It's ridiculous, and an army certainly didn't have so many distinctions. Also, about support units, it's rare that a unit had only artillery or only anti tank, etc, and it should be a mix.
If we take things down to battalion level there were artillery only units (even if they got two different calibers), not a mix of art, aa and at (even if that might also be the case).