Your thinking is sort of on the right track, but going the opposite direction. It's true that there's a lot of us, but that also means we need more towers in a given area to support those people. Additionally, it means the national carriers have to put towers, and the backhaul for them, in relatively remote areas to support a much smaller number of people. Getting that infrastructure is not cheap at all. Verizon, at least, has been very aggressive at improving theirs.
As for why they're so expensive, the answer is simple: because people are willing to pay what they ask. Also, at least some of the cost is due to the phone subsidy most people (myself included) use. As you probably noticed, the initial phone cost is significantly cheaper than what you pay. I personally wish they would go to a model more like European carriers, but due to incompatibility between US carriers, it's unlikely to happen since you basically can't take your phone to any other carrier and expect to get equivalent service (if you get any at all!).
Oh, I do have a question after all: Why are the United Statian (sic) carriers so expensive? I always thought that everything is so much cheaper than here because there's so many of you there. You know, lots of people, less expense per customer to get the infrastructure running and all that...
Because we have no consumer protection laws to speak of, and everyone needs the new "ooooh, shiny" thing and are willingly to buy it no matter the cost or actual need (look at Gary, he's buys whatever the hell Apple sells no matter what it is). Carriers are dicks simply because they can be, the US Government won't do anything about it until it's too late, and people suck at math and don't understand hardware cost, and subsidy cost over the life of the contract.