I don't do SLS but you can look up its founder, Seth Riggs, on the web and there is a book that he wrote that I have yet to buy and read, but I will do so some time soon.
Like most singing things, people seem to either love it or hate it, and I'm not sure which of those I am as I haven't read the book, but I think that 'methods' can sometimes be misleading, in that someone gets hold of an idea and it's central to their philosophy, and they build a method around it and get people to endorse it.
I use the Estill model because it's a model of how the voice works. It's not a method. It's not perfect either, but the best thing I have in my voice teaching tool box to date.
Speech Level Singing is not long established in the UK as far as I can gather, but has a large number of adherents in the US. The US vocalist website has a number of threads about it.
I guess there is no one way to sing, and dealing with the whole person requires teachers to have a wide variety of resources at their fingertips. If SLS does that for teachers and students it can't be bad.
I think there is probably a conflict between SLS and the way I teach with regard to the height of the larynx and the music theatre sound itself. But conflict leads to resolution - and that can't be bad either.