It has nothing to do with competition. You could have as many competitors as possible and no one is going to put a cell tower up in a remote location.
It has everything to do with the lack of competition. US tax payers paid $4 billion to AT&T in 2004 for fiber to -every- home. And that was never delivered, yet they keep getting more money. This is regulatory capture.
I've been on tiny Indonesian islands far from anything that could be considered civilization, and they'll have cell towers more often than not.