The first person fired for wearing a helmet is going to be so damn lucky. That settlement money will end up being equivalent of several lifetimes with of work.
There is absolutely no way that their logic holds up in court.
Almost everywhere in the US is at will so there’s likely no successful lawsuit in the situation you describe.
Sadly, it’s likely the first driver who dies without a helmet will result in their family filing a giant lawsuit. But that payout will be paid by insurance that is probably already factoring in the probability of such a payout.
They might if a bicycle helmet was an osha recognized protective equipment. But it seems like the company did their homework and said it’s not. If there’s some regulation for helmets then it’s a different story.
My work doesn’t require a helmet, even though it would protect me. If I wore a helmet and my employer fired me, OSHA wouldn’t give a shit.