...all people that legally want to carry a gun may do so.
Seriously? What about the mentally impaired? What about domestic abusers? I could go on. The only people who need to carry guns regularly, apart from the cops, are... well, there aren't any.
Sure, you live in an isolated place, and you want a gun for self-defense? Fine. that makes sense. You work nights is a lonely and possibly dangerous place? That also makes sense.
None of that entails taking your pistol to Trader Joe's. Of course if you did, and were discovered, you'd be thrown out. Yes, the owners of private businesses DO have the right to reject clientele they don't like.