Graft aside.....
I would argue the mayors lacked the authority, the wherewithall, to get volunteers to do the mental and physical work necessary to do the job. The mayors couldn’t force a disorganized populace to act in a functional manner.
It happens in all such disasters. Most locals just plain lack the organizational capability to function
You make a good point! But I’m still betting corruption.
Getting the military in there early is probably a good thing. People are so stressed with just helping their own families survive, that they probably do not have much energy for going to Mayors to volunteer to move bulk supplies around. The link below lists a lot of true? statistics about how much is and is not working now. You can check yourself, but I think it said only about 1/6th of the roads had been cleared. Water is also in short supply for many, not to mention food.
https://www.axios.com/85-of-puerto-rico-is-still-without-power-2494753594.html