And you don't even need monopoly to tell a similar story. If, for example, energy producers are at capacity - there is no way to squeeze out anymore kilowatt hours, or not really - then capping energy prices will reduce profits without reducing the quantity supplied. With a vertical supply curve, the price can go up up up up up without providing anymore energy. Just ridiculous profits.
Similarly, there are a roughly fixed number of hotel rooms reachable from the Florida's Gulf Coast. Letting hotels increase their prices won't add any. Capping prices wouldn't reduce the numbers of rooms available, just reduce their profitability.
No one model is "right," they're just ways of representing and thinking about things, but sometimes the lesson of one applies a bit more than the lessons of the other. By excluding the monopoly model as a tool, you can arrive at solutions that are wrong. In The Discourse, saying things like, "sometimes, price caps (or rent caps, or, for monopsony, minimum wages) are Good, Akshually," makes you a deeply unserious person. "Obviously, you don't know anything about economics," some internet glibertarian, or the WaPo "fact checker," will smugly assert, but it's right there in like week 5 of every econ class.
No one model is "right," they're just ways of representing and thinking about things, but sometimes the lesson of one applies a bit more than the lessons of the other. By excluding the monopoly model as a tool, you can arrive at solutions that are wrong. In The Discourse, saying things like, "sometimes, price caps (or rent caps, or, for monopsony, minimum wages) are Good, Akshually," makes you a deeply unserious person. "Obviously, you don't know anything about economics," some internet glibertarian, or the WaPo "fact checker," will smugly assert, but it's right there in like week 5 of every econ class.