Shouldn’t the normal size be 2? Given, well, the name?

You’d think so, but no.
Short story is the ‘nominal’ size is the size before going into a planer to smooth the faces.
Yes, it makes little sense, like many things related to construction stuff.

It’s actually purposely milled to be under the nominal dimension because it’s designed to be 2"x4" once the plywood or sheathing is applied. It’s makes it easier to get walls that are the actual desired thickness.

This one of those things that sounds correct, but isn’t even remotely true. Like not at all, not even based on anything even.

Wall finishes varies in thickness, and the milled wood also varies in final dimensions depending on moisture content.

Wall finished vary in thickness wildly

When I was designing kitchens, I and literally everyone in the construction industry around me all assumed that drywall was 1/2”

Fire rated partition wall? 2 layers of 5/8 each side for a total thickness of 6”