iTunes/Apple Music (where you can literally pay per track), Spotify (pay for streaming access and some other stuff), bandcamp itself (the web page is the player. purchases are also available within android app), are all music players where you can buy music and stuff, with decades of history. iTunes goal was literally to purchase music and play it, all in the same player program, and that's been released over two decades ago. Countless web platforms of different scales offer buying music (album or track by track) and function as a player as well. Amazon still sells mp3s in that way, and Amazon Music website is both a music store and a music player. There's a long history and wide variety of platforms with a goal of both purchasing and playing music, all within the same surface, be it an app or a web page.

What's next, arguing that these aren't actually "music players"? that paying for streaming access to music isn't actually paying for music?

There's just a variety of music players with different goals. Some players' goals are to prevent people from buying music or even discovering that they can pay for music. Again, with bandcamp it's not even removing bad third party ads or anything, it's just removing a purchase option, when it very often doesn't even prevent you from listening to music for free anyway, or sometimes even just downloading some music for free.