AT&T and Verizon DO NOT put LTE on every tower. Sprint puts LTE on every single tower in a market. AT&T and Verizon use 700 MHz which travels much farther than Sprint's PCS 1900 MHz so if Sprint where to deploy LTE like AT&T and Verizon are you would only have little islands of LTE coverage that probably only cover 1-2 miles each. You can put 700 MHz LTE on one tower and have it cover 10-15 miles in every direction with little to no dead spots.
9 cell towers can likely cover the entire city of Cleveland, Ohio using 700 MHz, but that doesn't mean it's going to be fast because they will have 200-350+ devices connected to each sector in the cell instead of 50-100 like Sprint will with the way they're deploying LTE.
As far as I know deploying 700 MHz LTE on every cell tower will cause interference and service degradation with LTE because it only performs to spec in very low noise environments.
AT&T's LTE coverage doesn't really extend past where Sprint's does even in areas where Sprint hasn't completed a market and AT&T has.
Here look at a comparison between AT&T and Sprint in Chicago »imgur.com/a/dDvTM