> I was surprised because I always considered them to be the worst physical medium for music.
That's a big part of why they're cool.
Imperfection is beautiful. We feel this intuitively when it comes to loving someone, or when it comes to impressionistic art. It really is the same thing with music.
I believe the typical response is that you can simulate that imperfection on digital media... but cassette lovers would argue this is tantamount to putting a photograph through a 'Da Vinci' filter in Photoshop. It's missing the point. There's more to music than what it sounds like. Where it came from, what you did to play it, these are all part of the experience. The context of a piece of a media, the means by which you listen to it, where it came from -- these change how the music feels, even if there is no difference in how it sounds.
Back when vinyl or cassettes were the only option, sure, the response is "screw your romanticism". But now that we have perfect digital media always available, there is romance in getting to choose something fragile and imperfect and precious. People like that feeling.