The problem for most of them is the time before "You get less black eyes after a while." Probably less of an issue if I make them wear gloves with more padding (I start them on very light sparring, using just those fabric-and-foam jobs, to reduce the bruising on rib hits).You get less black eyes after a while. And I have found nobody really cares that much. Hell we train with a model. And she spars.
Otherwise yeah make them wear the hat if they are that concerned.
For me, it's just the glasses thing. Those are a *****, even if none of the hits ever lands with any power. Hell, I bend them up once or twice a year, myself, just demonstrating an arm motion for a technique. I prefer to spar without headgear most of the time, but the worse my eyes get, the more the glasses matter.