If an employer wants to search every car every time it enters the parking lot, fine.
One, I can't do this.
Two, how would I know what you have in the privacy of your vehicle?
The liability comes into play if something happens while you are on the business property and act improperly to violate the rule. As long as it is locked in your car, it's not an issue. Once it leaves that sanctity, is another matter. The hope is you are responsible.
It all boils down to costs for insurance to keep the business alive. Not having a rule like this increases the premium to an outlandish sum. Look how many companies have this kind of requirement for hiring. the problem they have enforcing it, is invasion of private property.
And try saying you have a right to privacy on a military post as a civilian. See how that works.
I ran a private- no walkin gunsmithing business out of my garage. My premium was higher than the gross I made each month. That was a 60 hour + week. When I ended the business, my insurance was cut in half.
There are places where any vehicle that enters will be searched. The costs to an employer of searching all employee vehicles would in many cases be prohibitive, and an employer who insisted upon doing so might have to pay employers a premium to accept such treatment, but the fact that employer wouldn't want to spend the money to implement a policy does not imply that the policy would be impossible.
Note that while an employer might be able to impose such a policy for a particular parking area, the parking spaces within such area might not be tallied in the minimum parking space requirements imposed by zoning ordinances (i.e. if zoning ordinances would require that a particular-sized business have 100 parking spaces, it may be required to provide a minimum of 100 parking spaces without weapons restrictions in addition to any spaces it provides with such restrictions). The spaces with restrictions might be nicer or more favorably placed (e.g. indoor instead of outdoor) but the unrestricted spaces must still exist.
Two, how would I know what you have in the privacy of your vehicle?
As noted, you have a parking area which restricts entry to vehicles that will be searched; anyone who doesn't want their vehicle searched must park elsewhere.
Frankly, I would expect that very few businesses would find it worthwhile to have a restricted parking area, but if one did, so be it.