@joshdons I am so glad that you pointed out the issues because they annoy me too much to take the book seriously XD
In all seriousness though, I haven't read it myself, but what I have read of it, it sounds very similar to Jean Liedloff's The Continuum Concept which was written in the 1970s and I read in about 2008/09 when my first child was born. I loved it and it was probably one of the major influences on my parenting. (I'm sure in hindsight it has similar issues, but I didn't notice them at the time.)
I don't live in the US but I did live in the UK at the time, which has a fairly similar parenting culture. My approach was this: I tried to be specific or praise effort rather than results. I didn't worry about what other people did since I figured that it was most important that I modelled it since I was his main caregiver. I was a SAHM for 2 years (I know not everyone has this option) and when I was looking at daycare options, I prioritised those that seemed to share my values in this way and would have the kind of supportive environment that I valued. So in the end I was choosing between a childminder (I think you call this in-home daycare) who was practicing what I thought of as gentle parenting, she called it positive parenting. There was time out but only rarely, and that was a lot better than many other options at the time. She took the kids around to everyday activities like grocery shopping and school pickup, they had opportunities to play outside with more unobtrusive supervision, a lot of undirected play, a mix of ages. And the other option I looked at was a Montessori nursery school. I went with the childminder and later after he turned 3, there was a lovely relaxed learn-through-play pre-school which continued the same approach through the first year of school, so he would not really start classroom type learning until age 6 (and again there was a mix of age 3-5 in his classroom).
I don't think that totally unsupervised kid play is as safe or idyllic as made out in books - you can find tales of this kind of thing galore if you look at memoirs or similar of generations who were allowed to do this. I don't know if it's something inherent to groups of children because of some developmental lack of empathy, or whether it was linked to harsh physical discipline that was commonly used at the time and they were just acting the same thing out, but it seems to invoke a heirarchical structure upheld by violence. And if you look at cultures/times where children were or are left unsupervised for long periods of time there are unacceptable (to us) levels of accident and injury. So I think it's important for kids to have time where they can learn from each other and be autonomous without adult direction, but I do think that adults need to be aware (unobtrusively perhaps) in order to ensure safety and fairness.
I would say that it's not really a "method" as such so I would struggle to say whether it is "effective" - the most effective parenting book I've ever found is the How To Talk series. That's immensely practical and useful IME. The continuum concept just gave me an insight into the fact that different values other than the default parenting values exist and I happened to like most of these ones and adopted them.