The helmets weren't intended to stop a bullet. Glancing rounds it might shrug off, and a small caliber round- say, a 9mm pistol round- could struggle to deal with it, but in broad terms those helmets were about stopping fragmentation, shrapnel and whatever other random crap gets kicked up in a fire fight. Full rifle rounds or, say, machine gun fire would not struggle to deal with it. Nor was it really intended to- soldiers were trained to fire at the center of gravity, not someone's head.

I noticed during such classics as Saving Private Ryan that some soldiers (major stars) took off as often as possible.

It's Hollywood, but if you've ever worn the things you'd know they're less than comfortable. If you've seen the inside of it what you get is a lot of straps- stemming from a one-size-fits-all design- but not a lot in the way of padding, which means you're feeling every last thing that helmet bumps into. It'd make sense to take the helmet off in calm period. It wouldn't stop a rifle round and if someone was firing artillery or mortars on you, you'd probably know it pretty quick.