By insurance, I'm referring to Liability Insurance. I get the concern. I can also appreciate there being a question of property rights of the employer. If I owned my house, and I was anti-gun, I can tell someone not to come in to my house with the gun. It's my house. The company's place of business fits the same ruleset.
In your example, if the window washer drops a tool from the 20th floor and it falls on the head of someone on the street, killing them instantly, is the company any more liable if the tool was a handgun vs. a hammer? Is the person any more dead? If wearing a firearm posses a danger due to the work involved that itself makes sense to me. If you repaired high voltage transmission lines, wearing a metal sidearm seems counterproductive.
A company does not have liability of their guest's actions. Take a restaurant. In Virginia, you may open carry to any restaurant, and conceal carry to those that do not sell alcohol. If a shooting takes place in the restaurant, the restaurant isn't liable for the action of its patrons although the individuals involved would be. Would a company enact a policy for its employees granting them more freedom than its own employees?
There is separate liability even if you do ban weapons at a workplace. Any company can be visited by those that are legally armed. Should a gun policy ban the carrying of weapons by off-duty police? What about customers coming to visit when they themselves may carry a firearm as part of their job? Does the company ask them to take out their loaded firearm and ask them to put it in a storage container or safe? We have out of town guests that fly in, use a taxi to come to the office, and a taxi to leave. In that situation they can't just keep it in their car. Seems like even if you have a ban on firearms, you still need to have a policy of what to do when one "shows up". Handling a loaded firearm outside the holster to me raises the liability factor substantially as the likelihood of an AD goes way up. In that case the company should be named party to the lawsuit as it was their policy that led to the AD.
To be clear I'm not arguing that laws are enacted to trump property rights. I'm suggesting I'd rather understand and promote work place policies that achieve what each interested party would want. I have an underlying assumption the owner or head of the company is at least neutral if not pro-gun in setting these policies up. If less than neutral I don't see there being much the individual citizen can do other than accept it or find an alternate place to work.
Of issue to me is finding a policy that makes sense. The policy should reduce or transfer liability of the company, making the actions of the individual the same as their actions as defined by state or local law. Some places cite a "safe work environment" requirement out of OSHA and that allowing weapons violates that. I don't know the history of that rule, but I'm sure it was intended to say that the floors shouldn't be caving in and the water shouldn't be poisoned. To me a safe work environment would be one where if I choose to take an active role in my personal protection that I am allowed to do so as long as I meet state and local laws.
So the question is still out there. Does anyone have any sensible work weapon's policies they would like to share that address this?