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.
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.