As a recent transplant from New England, I am impressed with the extent of the arterial system in Tucson. It isn't perfect and the traffic signals aren't consistent (permissive left turn on green here, flashing yellow arrow there) but it gets the job done. At least this time of the year, I haven't seen any significant delays, even driving across town on a Friday afternoon. We'll see if that holds true during the winter.
I'm not sure I can think of any major ways to improve the current setup. It seems to be about as perfect as it gets, as far as operations of traditional arterial streets gets.
If I had one interest, it would be whether they could install a triple left turn with permissive phasing. Never seen this in the US before.