To start with, we already know that a permit holder (for example) from Florida is subject to tighter rules when he goes to North Carolina, let's say. (Fill in states of your choice.) Sometimes a permit holder is subject to less restrictive carry laws when he visits another state.
Not only would we have to keep track of the carry laws that pertain to us in the states we visit (which is what we have to do now), but what would govern our conduct and our carry in states that do not have shall-issue-type carry laws?
If this is intended to allow us to carry in MA, CA, IL, NJ, NY, what would the stipulations be? If there is not even a single, unified set of stipulations between FL and TX, what on earth would the set of rules be for a national reciprocity that allowed a FL CCW holder to carry in IL?