When you spar wearing hand protection and no head protection, a light punch to a sweaty forehead will slide off with no injury. However, if you were wearing head protection, the glove would grip the soft plastic of the head protection and snap the head backward. This happened to me a few years ago. The punch snapped my head backward, gave me a concussion and partially detached a retina. After this, the punch (and probably other head snaps over the years) lead to neck aches and a later diagnosis of degenerative disk disease in my neck, which as seriously curtailing my sparring.
Therefore, head protection may protect against certain types of injuries, but they may acerbate other types of injuries. Depending on the rules where you train, it choice is up to you.
In the United States, we have more lawyers per capita than any other country so they lawyers must struggle to find clients. To make a living, civil law attorneys cannot wait for clients to call them, they have to contact possible clients and convince them to sue. Thus, we have become one of the litigious counties in the world. This means that every martial art association, school, and instructor must do everything conceivable, and sometimes inconceivable, to protect themselves against lawsuits. For example, they have release agreements that inform you that if you spar with another person, you could possibly be hit and could possibly be injured. Duh! They may even be required to tell you that the sparring equipment is made of vinyl, just in case you may be allergic to vinyl.