By and large, business owners aren't dumb. They know the signs aren't going to prevent them from being robbed. The main reason for posting such signs: liability... liability... liability.
They're not keen on being sued in the event one of those gun-fiddling fools comes in, has a negligent discharge, and injures someone. Also, many businesses -- banks, for example -- have a standard policy that employees are not to resist if they are robbed: they'd much rather the tellers just hand over the money than get caught in the middle of a gunfight. There are both liability and workers' comp. concerns there... (actually in both those cases) -- so they'd rather not have armed customers who may want to play hero in such a situation. Not everyone with a concealed carry permit necessarily has training in using deadly force in such situations, so from the point of view of a business, it's a valid concern. (As far as I'm aware, in most jurisdictions even off-duty police officers are taught not to intervene with force in such situations -- and they do have training.)
Robbery is what they're concerned about -- that's more likely by far than some sort of rampage shooting. They're just playing the odds on keeping their employees safe, and their own exposure as low as possible: if it's just a matter of money, hand it over and write it off.
Just respect the sign and move on.