The flipside of this proposal is obvious. If the least regulated state can issue a permit which all other states must then recognize then that single state controls the entire country. Example:
State A decides under say NRA pressure to have a policy that all persons age 12 and older can sign up at their local super market for an automatically issued permit. That state decides that this permit is a separate concern from buying a gun and leave the regulation of gun buying to the present federal statute. No ID to get a permit, no background checks, no insurance requirement, no citizenship requirement, no felony, mental health, or spousal abuse concerns. There just is a form you sign saying I am not restricted from possession of a gun, and the permit is issued.

Why should all the other states recognize such a permit as valid when those other states want to have better control over the guns in their states?

How about instead a proposal setting minimum standards and they would include:
Requiring a course on safety
Requiring rules on storage and trigger locks
Requiring insurance [should be cheap as CC holders never cause problems or have issues with their guns]
Requiring proficiency testing
No automatic issue for cops or military
Full background checks including mental health
Requiring holders to submit to random drug and alcohol testing
Requiring psychological screening every x years
Requiring disclosure of charges not just convictions for domestic abuse.
Automatic forfeiture of your permit if you "lose" your gun, or leave in the bathroom at Mc Donalds, or accidently shoot yourself while demonstrating the gun for a friend, or take it through TSA screening or in any other way demonstrate that you are less than 100 percent safe with your weapon.

I could go on.

I thought those on the right were totally in on State's Rights?