I really only use open fronts if I have a horse prone to knocking rails. And if that’s the case, I usually leave him naked so they learn not to be too casual over the fence.
What size are you jumping? Not to sound too cavalier, but I don’t usually pull out any boots at all unless they’re jumping more than 2’11, they’re wearing studs, or I’m at a show. I know it’s boarding-barn normal for people to pull out all the stops for a jumping lesson, but it’s usually unnecessary especially in the heat.
I don’t see why brushing boots wouldn’t be okay. You can pick up the fleece lined Sport Boots at Dover for like $20 when they run fall sales. They wear really well and are indestructible. If you’re not into the fleece (understandable) they do have knock-off Woof boots which are perfectly fine for schooling.
I certainly wouldn’t say horses don’t hurt themselves that way, but it is rare. Of course, it is also one of those things where an ounce of prevention is worth a pound of cure.