Many college coaches think a mask means mental weakness. I know at a nearby BIG XII school, the coach does not like to take players that wear a mask. That's just one but there are many like that. There are also HS coaches that think this way as well.
As long as I am paying the bills, DD will have a mask.
A coach should absolutely be allowed to take this position, but only after willingly taking a line drive off the face from 35-40 feet away. If you're tough enough to stand there and take it, then fine, make your players go without a mask.