Tearing up the road is a good idea. It always bothered me that the Alexandrians on Walking Dead didn't think of that. Tearing down all the signage that pointed to their location at the very least. Especially while they had the equipment and stuff.
I don't know that water is going to be a huge problem in AZ, though. I think it's possible AZ might get more. More of what's beating up CA will inevitably make it over the mountains.