There's another place 'of' doesn't really belong.

When you ask a question like "how big of a car is it?", it's actually supposed to be "how big a car is it?". But the first one sounds right to our generation, while the second sounds right to older people. So at some point we randomly put an 'of' in there that doesn't give any meaning or serve any purpose. structurally it doesn't belong there either.