Here, in Indiana, those signs don't give a business the power to trespass you out. They can do that already, for any reason they want. They don't need a sign for that.My take on it is that they are signs created by head office (which may be in some haplophobic state) to standardize firearm policy countrywide, ignoring the fact that, say, semi-rural Indiana is not the same place as Los Angeles. The signs give the mall the power to trespass people out if they're making shoppers nervous, and I think that's the main point - especially for the signs that are specific about "no open carry".
One thing this incident sure taught me is that the news morons do _not_ understand preemption laws. "OMG they had a no guns sign, he was carrying illegally". No he wasn't. In Indiana, those signs have no force of law. I can put up a sign that says "You MUST be wearing green underwear to enter this mall". Unless I check, I won't know what you're wearing. If your pants happen to fall down, and you're wearing tighty whities underneath, all I can do is say "I don't want you on my premises, please leave", at which point you must leave or I can have you arrested for trespass. In the case of someone concealed carrying in "violation" of one of these signs, that conversation won't happen until after the shooting finishes. Ergo, those signs can and should be completely ignored.
(this does not apply in regions, eg Tennessee, where private "no guns" signs DO have force of law. I really hate having to leave my EDC in the car when I'm shopping in Nashville, but there you have it...)