Back in 1970's when I got my CCW, NYC played the "oh- we just ran out of applications so you will have to come back to 1 Police Plaza another day" game. I heard that for 6 months until a lawyer sued them into giving out the permit application.
Then if you used the wrong color ink to fill it out, missed dotting an i or crossing a T, they threw out your application - you had to get another one (about an inch thick) and start all over again. It was also very common for them to "misplace" the properly filled out app. (in triplicate BTW) and once again had to start the process all overall over. If memory serves, I think the app fee was $400 at the time.
Where we live now, a law abiding citizen of the State gets a CCW application approved and delivered in 10 - 12 days at a cost of $45 for 7 years. Renewals are done online in 5 minutes. BTW, we are now a Constitutional carry State, but the physical license does have some advantages such as out of State carry in many other States + more.