Obesity correlates with several chronic diseases, and so body fat percentage must as well. There are certain diseases where elevated risk is directly associated with fat specifically (I remember seeing something where heart disease is affected by abdominal fat in particular) so at least sometimes fat matters, and not just mass.

Note that it doesn't necessarily imply any kind of causality.

I think "health" is a nebulous concept anyway -- in my book, you are "healthy" if the physical state of your body allows you to do what you want to do.