"I have seen the opinion that that's not really classical monopoly behavior, which would consist of keeping prices low in order to discourage competitors from entering the market, so making it a source of low but steady and reliable profits for the incumbent. Duopoly has different dynamics."
Monopolies only keep prices low to drive competitors out of the market, then jack prices up high to the profit maximization point (i.e. the point where $ per customer x number of customers yields maximum dollars.). There can be two of these points, one lower $ per customer but more customers, and the other higher $ per customer but fewer customers, with both being higher than a free market would have.
That said, the US market is no monopoly. Don't get me wrong, I'd like a more competitive market, but it simply is a very very high barrier of entry to be able to run enough cell sites to even cover a region, let alone the country. (MVNOs are another matter but they are run at the pleasure of the big 4...) The original buildouts (1980s), if the coverage started out spotty... well, tough, there was probably nobody else to go to, they could build out over time and get plenty of customers to fund it. Now, if you started even a regional carrier, you'll have trouble getting enough customers with a lesser buildout, to fund completing the buildout. You could need $1 billion or more to build out a regional network, let alone national, and very few investors would invest in this. After all, VZW has been spending like $4-5 billion a year at least since 2000 ($75 billion), AT&T something like that, and even if T-Mo and Sprint have been spending $1 billion a year (I think it's somewhat more than that) that's $15 billion since 2000. And these carriers are older than that actually.