Yeah, I could see the brim being useful for shielding from the sun, but would probably want to use a shape like a pith helmet instead:

That way the brim might actually even offer useful protection, although should still test that it's not dangerous when you fall off a roof or whatever. Could probably just make the brim out of cloth in that case, though.

Brim ish to prodect da sholdah /s

From wearing regular ones (okay many years ago working in wood sort of mills/production but not long either) I'm not sure the divot would make much a difference if proper clearance from sides to the inside harness, though guess may force impact in a way not intended for proper safety gear.

Still doesn't seem quite right to me, cause you wouldn't want your head knocked to a side if the brim was hit.

Probably a reason they were never designed in that way.