Actually, if you check (NRA-ILA gun law summary for AZ), you'll find that carrying "out in the open" requires no permit. Only carrying concealed.
The original prohibitions on concealed carry assumed that only someone up to no good would hide the fact of being armed. Then, in most states, they decided that carrying openly was "threatening", "disturbing" or otherwise against good order or some such claptrap, and banned that as well.
Actually, I realized after I wrote my comment that I misspoke. Thanks for the clarification.