It doesn't matter if they are allowed to, as some folks would do anyway.
A problem that I have with constitutional carry is that if you're involved in an encounter with police, they police have no way of easily checking if you're NOT allowed to carry a firearm. With a permitting system, they can easily check. Tens of thousands of firearms are confiscated by law enforcement every year when found on the person of people that are prevented by law from carrying. Tens of thousands.
That ability goes away in constitutional carry states.
I do not see it as an unreasonable system to require people go through a permitting process. I'd also like to see universal background checks required for all firearm transfers: private, public, hand guns, long guns, all guns. That way the police could check the person that I want to sell a firearm to and confirm they're legally able to own it before I make my sale. There's just not a good enough reason to not do that.
It's proven that background checks work to keep firearms out of the hands of people that cannot legally own them through sales at gun dealers, so it should be extended to all private sales.