I saw the results of torrential rains in the Phoenix area in the early 80's when flying overhead. Rather amazing i should say...
I have lived in the Phoenix area for over 40 years. Back in the 80's the roads would be a mess and the canals would overflow. 35th Ave would turn into a virtual river due to any significant storm. Whole neighborhoods would be flooded.
The canals were made to distribute water so they lost capacity as you went downstream. This is not a good attribute for channels intended to divert water away.
Since then they have put in storm drains, at least in the northwest valley. Additionally, they have added a lot of open drainage ditches which are capable of carrying the water away.