By the same token all states allow handgun ownership but their are procedural differences in how you obtain a carry permit and different rules for carrying handguns after you obtain a permit. Even after you obtain a permit a citizen can't carry handguns on any military base, in a sports stadium, city hall, courthouse or airport terminal.
It's interesting to me that in almost every case the same people that argue that an individual state should have the right to decide whether a same sex couple married in another state is legally married in their state will argue that they should have the right to carry a pistol in their hip pocket in any state they want.
Regarding the prohibitions mentioned in the first paragraph, that's not completely accurate. One state recently permitted gun carry in government buildings (can't remember which). The prohibitions against carry in schools is rapidly weakening also.
Your second paragraph is interesting. I could go full libertarian and claim the state as an entity has no right to tell me whether or not I can carry. Neither New York, nor California, nor Texas for that matter. Licensing carry is nothing more than a revenue grab. It costs me $110 every renewal now (every four years). Why? The government is already taxing me (county level) for the employees that handle the paper work. Just another way to squeeze the tax payer. And if a state or locality (if not preempted by state law) wants to eliminate carry, that is their right under the IX and X Amendment. If they want to handle it the way Michigan does, that's their right. Don't like it and it's important to you? Move.
But, for the sake of argument, let's accept that the state can license. Why should another state honor concealed carry when it violates their own laws? Does that mean that whatever is passed in one state automatically becomes the law in every state? So that when I fly out to California from Michigan, I can transport my weapon per Federal regulations then load up and carry while I'm there? Okay, assume that's legal. What about the residents of the state? Can they now carry? If they can't, doesn't that run afoul of Equal Protection Under The Law in XIV Amendment? Personally, I don't think the Founding Fathers envisioned one state driving the country. Ever.
Same argument regarding gay marriage, til SCOTUS made that argument moot. Or Roe v. Wade for that matter. If both those atrocities get reversed, the power revolves back to the states. Where it belongs. So you could expect to see both gay marriage and abortion legal in some states and not others. Which is as should be. The PEOPLE decide. Not the Feds. So, absent the heinous SCOTUS ruling, should one state's law obligate another state to recognizing said "marriage"? Nope.
I'll go full libertarian again and question whether the state even belongs in regulating marriage. Marriage is a contract. Think not? Don't both parties have to sign a marriage certificate at the time of or shortly after the ceremony? Why is that? Because it's a contract and by signing, you agree to certain obligations, e.g. children, asset obligations, etc. Different states have different views of said obligations under the marriage contract. Which, again, is as should be.
You might argue that terms of contracts should be honored among the states but I think that is for them to decide, certainly NOT the Feds.
By the way, someone brought up the Reciprocity passed the House of Representatives. My answer is --- so? Did it pass the Senate? Did Trump sign it? The fact that it passed the House, along with about $4 will get you a cheap cup of Starbucks.