Dunno much about body-weight "cults".
Maybe some people travel a lot--perhaps to places that don't have gyms, such as the wilderness--and want a regimen they can practise anywhere, without having to depend on the availability of facilities and equipment.
My Goju training came from the Mumei Dojo in Shenandoah Pennsylvania. I learned Sensei Carla Pronio , who learned under Hanshi Ron Martin and I forget who exactly came after him( due to financial issues I haven't been able to train and some things have slipped my mind), but the line does lead to O-Sensei Chojun Miyagi. We are under the IKKF for competition. It's a small town but our classes have been fairly large. Our dojo is tiny, but we do accommodating classes up to at least 30 students, but with Sensei and 2 Senpai on the floor at all times.
And reading about the free weights being better than machines is true. If you lift a barbell freely, you have to try and lift the heavy weight WHILE making sure it doesn't tip and you lose balance falling, dropping the bar and maybe falling of the bench causing injury. The machine takes away the need to control it because it's already held in place, and you don't get to work anything extra besides isolated muscles. Along with Karate I was on a high school football team, so I understand some things about Weight Lifting also.