As someone who lives in South Florida (east coast, Jupiter southward), I can state that the only toll roads in the area that also have service plazas are the Florida Turnpike (north/south and can be used for commuting) and I-75 west of US-27 (runs east/west across the state, and at the point it becomes a toll road, you are basically heading away from the population center towards the middle of the state; also, practically no one lives west of US-27 until you get to the west coast of Florida). The other toll roads (Sawgrass Expressway, 924, Dolphin Expressway, parts of I-95 in Miami, Don Shula Expressway and I think 826 (it's been awhile since I driven that one)) are all very short (longest is the Sawgrass Expressway, at 20 miles) and all in a very dense urban setting and absolutely no service plazas.
Also, all the toll roads in South Florida use the same electronic system (EZ-Pass); it's also usable up through Orlando (from personal experience). With such a system, there's no need to even slow down to pay the toll (and there are no more toll booths in Miami; if you have no EZ-Pass system, a photo of your license place is taken, and a bill (not a ticket) is mailed to the license holder).
Edit: There are also three service plazas along the Florida Turnpike in South Florida, one in Dade County (Miami), one in Broward County (just north of Ft. Lauderdale) and one in West Palm Beach (towards the north end of the county), each separated by approximately 30 miles. Depending on where the cop in question lived and worked, he might have never even passed a service plaza (and besides, the gas there is more expensive).