Which permit were you trying to get? I just did the Subway last month and had to go through the same thing. I ended up planning the trip for a Friday in order to increase my chances of getting a permit, but that meant I had to leave Wednesday night and drive through the night to get to the permit office at 5am. I hate the permit system too, but I can understand it is a necessary evil. Without those restrictions, it would end up being like some of the other popular attractions where you would be waiting in line on the hike with hundreds (sometimes thousands) of other people. And for those slot canyons, it can become really dangerous to have a human traffic jam down there.

I'm sure you know, there are three different ways to get the permit. Reservations (which are usually booked months in advance), lottery system, and walk in. That means you really need to plan ahead of time, and it takes all the spontaneity out of the trip, but at least it does give other non-local people a chance of getting in. If you can, have multiple options so if your first choice is booked, just go down the list. If you're flexible chances are you will be able to get a permit for at least one of your choices. And if you go during a weekday, your chances are much better than trying during a holiday weekend.