Flower galls on Arizona Ash trees are caused by a tiny eriophyid mite that attacts Ash flowers, the Eriophyes fraxinivorus mite.
This small mite feeds on the male flower buds, causing them to develop abnormally. The small ball-like growths may be unsightly, but they do not damage the health of the tree and after a while they will fall to the ground.
One benefit is that these abnormal flowers do not produce pollen, so that may help reduce allergies.
These mites are difficult to control, so most people do not try to treat them.
Healthy Ash trees, not stressed by lack of water, are not as prone to infestation.
Case in point, there is a line of four Ash trees, same variety, the seed crop on three of them is huge and the trees are green and healthy with no flower galls.
However, the tree on the end of the line is yellowish, has some dieback in the center and is completely engulfed with flower galls, not a healthy seed can be found. The last tree didn't receive the same amount of water as the others. Stress causes multiple problems.