anyone hitting an individual with private security is going to do surveillance first and account for weapons anyhow.

Unless they’re surveilling with the intent of knocking out the bodyguards so they can give the target a stern talking to free of prying eyes, I’d imagine their only thoughts on the matter will be either “they don’t have guns, we should bring guns” or “they have guns, we should bring guns.” And for the firearms being barred portion, that’s going to vary a lot by locale and venue, but there’s always the option of locking firearms up in vehicles.

I think the most compelling reason not to have firearms is that if someone isn’t armed you don’t want them to suddenly become armed thanks to you. I’m just not so sure about the rest.