A big part of my job is overseeing contract preparations and limiting liability to my employer. I also supervise quite a few people and I need to limit their exposure to hazards in the field. I'm sure no lawyer and not an insurance guy though.
I am of the opinion that any such requirement is related to workman's comp claims and potential lawsuits from the family if you get killed.
They don't know if you maintain your gun properly. They don't know if it could fail and get you hurt while using it. They don't if you've been shooting nuclear loads through your gun and it is on the verge of a catastrophic failure. If you get hurt because they allowed you to use your own gun with no knowledge of how the gun is maintained, their risk goes up in court of loosing a very expensive workman's comp claim because they were not in control of the situation by issuing you your gear.
I am required to provide my personnel safety gear to use on the job. I can't let them use their own gear for the same reason. If someone's hard hat is expired, and they get hit in the head and killed, the lawyer is going to point that fact out and I'm liable. If the employee uses their own gear, and wears it out or breaks it, they may want me to replace it. I do not have the legal ability to spend funds on privately owned gear. So the employee could sue if I allow that situation to occur.
If they let you carry your own gun, and you decide you want to carry a Kimber Solo, and it jams when you need it, and you get hurt or killed, the court is going to see it as the company allowed you to use an unsafe and unreliable piece of equipment.
Stuff like this is all about limiting liability, and trying to project forward how a court might see it, or an insurance company might try to deny claims. It's that simple. Money...………… The actual legal arguments on the other hand can be very complex and go around and around when something actually does happen.
Legal arguments around hollow point ammo are likely moot at this point as law enforcement uses it everywhere. It's more likely a cost savings, and they may actually be trying to limit lethality, as the family of a dead perpetrator is likely to sue.