Almost any mulberry comes to mind. Not uncommon to see 10' or more growth their first year in Arizona.

Although I'd never plant one in Tucson, a cottonwood might work for you. However it will need a LOTS of water for maximum growth.

Ours went from a volunteer seedling to a 15 footer two summers later, with only lawn watering (this was in Illinois.)

It didn't seem to pose any problems other than the fact it was too close to the house, which is why my Dad ultimately removed it :(

Desert museum palo verde. It is beautiful, meets all your requirements and you don't have to baby it. Ours planted 3 years ago went from 6 ft to about 25 feet high today.

Red Push Pistache

Here is a link that might be useful: redpush

You could also try a thornless Honeylocust. They'll grow in pretty much any climate.

Thanks everyone
I knew I could count on my garden buddies.

Why not Sissoo? and folks please spare me the horror stories about roots lifting your driveway and moving it halfway across town. If you plant the tree properly, and water it deep and infrequently none of that is a problem whatsoever. I have a beautiful sissoo that I planted in my front yard in 2009. it is now HUGE, as tall as my 2 story house and very nice shade.

Never mind about Sissoo, I see you're in Camp Verde, and that probably gets too cold for them in the winter.

Thanks for the thought greendesert