Hard to catch a fly ball or foul tip at the plate with your eyes closed
I caught in little league for years before eventually switching to 3rd and I don't remember ever closing my eyes, but perhaps you're right, maybe it's just an involuntary blink that happens to get caught on camera. But, as you point out, the batter's eyes aren't closed.
Man, I sure learned to hate aluminum bats playing infield, though, that's for sure. Spicy!