I don't really want to be able to dictate what you keep in your car. I just want to retain the right to be able to dictate what comes onto my own property, which includes cars and their contents.
FWIW, my opinion is that if as a society we are actually going to trust ourselves to keep and bear arms, and so far, we do, it's still in the BOR, then as employers, we shouldn't worry about our employees being armed. I personally let my (very few) employees bring arms onto my property. If there was one I didn't trust with a gun, I'd let him go rather than tell him to leave the gun at home. Because then trust would be the issue.
More to the point, I worry that large companies who prohibit arms on their property are doing it out of a desire to be politically correct, which is reprehensible. Or maybe they fear lawsuits, which is a comment on the legal profession.
In spite of all that, I don't think government should be given the power to direct property owners in what their employees may bring on the property. Make that strongly don't think.
The contents of automobiles are beyond your "right" in many states. Your property rights don't cancel out my property rights.
My problem with banning weapons in the locked cars is a bit more pragmatic. I have worked at such companies, one of which had a force of private security for their facility. Unfortunately, the pricate security was not armed, nor licensed to be armed as part of their job. So, the employees were not allowed to be armed for self defense, and the security was not allowed to be armed.
The question is: How does this enforce safety? It doesn't - there is no "force deterrent" to the looney who violates company policy and starts shooting up the place.
Worse yet, the company admitted no liability if this happened. In other words, the company was allowed to disarm its employees without having to guarantee their safety from such incidents.
It's really a private-property (parking lot) versus private-property (car) issue, IMO. As such, it should be adjudicated toward the least intrusive solution as possible - as long as the weapons stay inside the vehicle, no infraction has occurred.
Just my $.02