All states, to the best of my knowledge, will revoke a resident permit on moving OUT of the state and you will either be issued or be required to apply for a non-resident permit if available. This is a good reason to have more than one permit.
A change of address without notification within a set period of time will also nullify your permit, resident or non-resident.
The concept of a national reciprocity bill, as with drivers licenses, makes it mandatory upon the state to recognize a permit issued, resident or non-resident, in any state of the Union, wherever your are in the USA, without recourse. End of story. I believe that in the beginning there were states that balked at reciprocity. That was quickly resolved by (a) the threat of non-recognition by any other state; and (b) the threat of withdrawal of any and all federal funding to the rogue state. All states fell into line immediately thereafter if I am not mistaken but I stand to be corrected on this.
A national reciprocity law should do nothing to legislate the requirements for the permit other than what is presently done (no felons, no whackos, etc.). It would only grant full reciprocity amongst states and stop making felons of good honest folk that simply want to travel with protection or for hunting. No further meddling would be undertaken.
Just my opinion but as a traveller half of every year, along with a few million others that do the same on a constant basis, it would be a godsend, especially if tied into the constitutional arguments; putting them to bed once and for all hopefully.