I say this as a big proponent of the right to self defense on a personal level, the current legal view is that, gun possession in the public square is not a right, it is a privilege, one that can be revoked as seen fit by the government. What is a right, is to keep and bear arms, this means one can maintain possession of their arms without fear of confiscation on their personal property or property in which they have expressed approval of the private owner.
This is why even as far back as the early 1800's it was not uncommon for local sheriff's to mandate a leave your guns at the sheriffs post at the edge of town policies. Yet, the local barkeep could still have a shotgun under the counter. Town was the public square, where the local bar, while a public establishment, was a private proprietorship.
Many of these type of rights extend from the pre-US castle doctrine laws which summed up shortly basically conferred the concept, that a person is king of their castle, the states rights should be significantly curtailed, when it comes to a personal private property. More modern day utilization tends to just boil it down to self defence, in ones private property, but historically it held a view which helped shape many of the personal liberties that were incorporated into the Bill of Rights.
Since nearly the foundation of the USA public possession has always been seen as a privilege extended by the state. In earlier times this was generally pathwork local law and the local sheriff view of guns carried in their town. Now it is generally more formalized via a state based licencing scheme.
A good read on rulings that imply it is a privilege:
https://www.governing.com/topics/public-justice-safety/tns-c...
Converse to the last paragraph though is that while precedence and the lack of challenges early on to public restriction lead to the concept of public possession being a privilege, the subject is now in modern day being battled out in the courts, and there have been some rulings ignoring history policy precedence
A good read on rulings that imply it is a right:
https://reason.com/2014/12/05/is-concealed-carry-a-privilege...
With all that being said, may issue is fraught with corruption and unnecessarily restrictive, in my state we have a shall issue and it works well, especially coupled with our strong castle doctrine laws. So well, that at the entry of my state an anti-gun group put up a billboard that said "Visitor's Warning - Florida residents can use deadly force". The billboards actually has the opposite effect than the group had intended so they removed them.
I would be a proponent of each state going to a shall issue system and extending the public privilege to a national recognition and reciprocity system, much like the state's driver licence systems are. That being said, it's fairly consistent that the state has almost since the beginning seen public possession as a privilege extended and not an absolute right.
A good read on the subject and precedence for public gun carry, from a purely historic perspective is this article:
https://www.smithsonianmag.com/history/gun-control-old-west-...
on a completely tangential rant, class 3 FFL transfers, require a sheriff's signature and are just as rife with corruption and cronyism. I used to live in a county where the local sheriff was very vocal about the fact that he would not sign for class 3's, yet every deputy or buddy, cousin or uncle had one. I would love to see the local law enforcement sign off requirement, for Class 3 be removed and rather just make it a duty to inform local law enforcement that one is in possession of a class 3.