What you said mostly.
Also, just as parents have the moral/legal obligation to protect their families, shouldn’t a private company that forbids legal weapons have the same obligation to protect those that enter?
Of course, private property is just that and we can chose to work there or not usually (I do/do not).
If I'm ever mugged on my way to/from work, my employer is #1 on the lawsuit list. I drive through a pretty lousy part of town twice a day. I'm unarmed because of my employer's policy.