Johan,
these days it's more for the nostalgia and fun than anything too serious. A bit like running old classic cars.
The fact that cassette, when done well, can sound really very good, and in many ways nicer than digital alternatives, is icing on the cake.
Me? I record stuff I really like off the radio, and also LPs to save cartridge and vinyl wear and to allow me to listen to them while cooking or washing and avoiding that "ker..chunk, ker..chunk" moment while your hands are covered in dough...
I have a whole bunch of decks, some restored and working 100%, others awaiting restoration. Yes, they can be a right PITA - especially my ZX-9 which has just developed a faulty cap in the PB circuit and has to go on an expensive trip to Bowers & Wilkins. Then there's the Pioneer CT-A9 that's just a service engineers idea of hell.
Oh, and I have a CR-3. A very nice deck indeed when properly aligned. Switching between Tape and Source even on a lowly TDK D without any NR it's almost impossible for anyone without "golden" ears to tell any difference (the slight background hiss is the give away). You can still buy the belts you know....