I agree with everything you've said regarding how the phone associates with a single tower at a time and such.
However, I was under the impression that the "cells" were only cells when they didn't overlap.
I can't speak for every city, but this one's "towers" aren't so much towers anymore. Most of them are little gadgets on the side of a building, or in the parking lot underground, or scattered everywhere. They don't just kind of overlap, they mesh, allowing a phone to pick the strongest/nearest/best/available one.
But hey, maybe I'm just harping on the four letter word.
In any event, doesn't it bother you to name things based on tehir particular implimentation instead of their function? It bothers me.