Cockroaches are very common in Albuquerque and, as you noted, are more likely to come into households as the seasons change. I doubt it is something the City can (or should) handle, but rather it is up to individual homeowners or renters. 

Personally I get a quarterly bug spray on our property (we use Preventive Pest Control) and make sure the bottoms of my doors are sealed well. Leaving doors and windows open are an invitation for bugs.

Ciaran