Do you find this is why most artists first choose to record to cassette, or is it because of other things like easier/cheaper distribution?
I'd pop a tape into a boom box, record the rhythm guitar part with my little "headphone amp" routed to the aux-in, then rewind. Plug a headphone cable in and split it so the right channel went to headphones and the left channel went into the left aux-in on the second boom box. That way I could record the leads or other parts while listening to the rhythm over headphones.
You could bounce back and forth a couple of times as long as you had some stereo-to-mono adapters but quality degraded quickly. Still, I was a teenager with a $100 guitar, some old boom boxes, and a lot of time.
Still, I can't imagine cassette is easier or cheaper to record and distribute compared to digital or even CD-R today. I'm guessing it has as much to do with "novelty" (which is funny to say about deliberate anachronism) as ease/cost of distribution.
That said, if people dig it, then more power to them. I like picking up vinyl records at Goodwill because they're 4 for a dollar and sometimes I find something that ends up being pretty interesting. I also buy vinyl new releases sometimes because there's something more psychologically pleasing about getting a "thing" for your money instead of a file that could just as easily be duplicated infinitely. I really like how vinyl often comes with a digital download code so I still get a 256-320k/sec mp3 copy for portability and convenience but I also get the big cover art and something tangible. Album art really is something I miss about physical media and vinyl 33's are large enough to offer great, big cover art.
1. A lot artists don't incorporate cassette into the workflow much. Usually people do what they do with a DAW or go to a studio to record. Cassette is mostly used as medium (like CD, vinyl etc). But yes, I do have friends who record directly on cassette. This will sound very rough though (depending on setup), too much even for some lo-fi aficionados.
2. Hipster points. Tapes are very "in" right now. Don't disregard this point. Just like networking is sometimes seen as a sacrifice of your "humanity", so is hipsterism. This is not so. Like it or not, sometimes it's important to go with the flow and play the field.
3. Easy/cheap to make. You do have to record in real-time which sucks when duplicating tapes, but other than that it's way easier to do a few tapes than to go vinyl.
4. People like supporting artists. This can be hard. Many shows are free, everyone downloads, so tapes, even if they can't be played at home, are a way to show your appreciation.
5. Sound. The sound is to me the most important part. Cassette can sound just as good as vinyl with the proper transfer, and introduces some great artifacts like a smoother high-end and a bit of saturation.
6. Professionalism. If you've spent 20-50 hours to create artwork, order tapes, duplicate them (or get someone else to do it) etc etc you show that you're serious about shit. It's a way to create your brand (of course this goes for vinyl etc as well).
7. I'd just like to copy Coldpie's point in regards to vinyl further down in this thread. Go upvote him: "...for some there's more to listening to music than just listening to music. Going to the shelf and looking over the albums, remembering when you bought each album, who you've played them for, things that were happening while you listened to them. Looking at the cover art or the silly liner art or notes[1]. Noticing markings (or smells...) from previous owners and wondering about them, what they were doing when they bought or listened to the album. Physically placing the album on the turntable and aligning the needle. Listening to the lead-in scratches as you adjust the volume before the music kicks in. Sometimes you get silly lead-out loops[2]. It's just a fun, physical way to listen to music."
I guess the difference is that I make music as a hobby, and do it almost entirely for myself.
Personally I'd actually love to own a 4-track and do some solo stuff for the same reasons you described in your original post.