No, you would't expect that at all (other than a tiny fraction).

People don't seem to regularly hit their heads riding at all. It doesn't make any sense to expect they frequently ride with their heads closer than 2 inches to things.

It seems more than apparent that people overwhelmingly try not to ride close to things.

That is, one would expect that it would be a rare exception. Given that nothing is perfect and exceptions will always be found, the argument that helmets "increases the chance of banging your head" is kind of silly on its face.

It's another example of "if it's not perfect, one shouldn't use it" argument.