Phoenix residents tend to be more active outdoors and that puts a lot of pressure on the natural land resources. As shooters, we tend to be outnumbered by other recreationalists that aren't comfortable around guns and gunfire.
The desert north of Scottsdale used to be a great place to shoot, but there were too many hikers, mountain bikers, horesemen, motorcyclists, nature lovers, tourists, etc. complaining about the 'random' gunfire. Scottsdale solved the problem by annexing all the land north, right up to the Tonto NF. Since the land was now within Scottsdale city limits, existing laws prevailed such as no discharge of firearms. Pretty clever, right?
Even some BLM land (such as Table Top Mesa) has been posted as 'no shooting' due to high recreational use.
But there are still some good, safe places to go shoot. You just have to go a little further to get off the beaten path. Take a look at this thread on LRH from a couple years back:
Where to shoot in AZ?