He has a hair problem.
Why is the sentence not natural?
For a start, it suggests that he actually has some hair, and that there is a problem with it. If he has hair, he can't be bald. Secondly, we simply don't refer to being bald as a problem or a challenge. It's a natural process that affects people at different ages. Younger people might consider it a problem but only in aesthetic terms.
I was going to mention "folically-challenged" as an amusing way of referring to baldness, but jutfrank beat me to it.