I started it because I'd repeatedly burned out of full-time jobs. Working 3 days/week was a great 4.5 years for me, far more rewarding than the added salary I passed on could have been. Aside from lower work anxiety, I had time to write two books, give three conference talks, get engaged, get married, take up several hobbies, and enjoy life thoroughly. My work has been overwhelmingly better: I stay out of rabbit holes, I recognize deep patterns, I prioritize ruthlessly, I deliver the things my users didn't realize they need. It's not magic, it's just downtime for my unconscious to noodle around with problems without pressure.
I think working part time is a hugely valuable experience for anyone who doesn't have a pressing need for dollars in the door (eg to pay off US medical bills or student loans). There are plenty of blogs out there on frugal living + investing (I recommend MrMoneyMustache and Bogleheads wiki), so you can live comfortably and still save significantly towards retirement.
I can't argue the financial math of why it rarely works, but I'd do 3 or 4 days a week again in a heartbeat. (15 year dev, currently Rails/Django/Haskell, Chicago/Remote, peter@valent.io if anyone's looking.)