I keep seeing references to this from Americans, but is this actually a thing? There’s no way my ISP would allow me to connect a device that isn’t owned by them.
When Americans complain about Comcast, it's not a meme, they are actually an awful company.
But for the record:
If you just sign up for Comcast (XFinity, whatever) and use the internet, you are renting a modem/router combo from them for about $10 a month, in perpetuity. You can buy an off the shelf modem/router for a couple hundred bucks, and use that instead. It'll pay off in a year or two. You have to call Comcast up and activate the device, but it's otherwise a completely painless process.
Further, my experience with Comcast specifically is that every three months, they "forget" that I don't rent a modem from them and just start charging me the rental fee anyway. Then I have to call them up to tell them to remove the charges and stop adding new ones.
Here you don’t pay a fee for the modem but they don’t let you run your own. Among other reasons because they want to force retire unsupported frequencies.
EU rules do not necessarily demand it - it depends on how exactly things are structured logically. They do demand that what you connect to termination point of ISP network is your decision, but that termination point can be a cable modem for example.
Shades of pre-1968 AT&T. "Oh no, you can't connect that modem to our lines." In fact, prior to late 1956, AT&T even told people they couldn't mechanically attach a device to their phones.