I am a (British) Montessori (elementary) teacher. (Coincidentally in Switzerland too!)
Happy to answer any questions as best I can, but if I would always recommend that you do some research, and read some of her books/papers.
I don't agree with the cult/purist side of things but I do massively appreciate the materials, the programme and the autonomy of the children.
You can see the difference in the children... Children who join our school from the public system are not autonomous and we have to spend a lot of time getting them into the habit of choosing their own work, rather than waiting to see what the teacher will give them for that day. They really struggle to work for themselves, rather than the praise of an adult. The maths program is incredible and very advanced of the public curriculum. Plus a large part of the program is to build a community spirit and create a balanced adult.
But, in the UK, the education system is very child centred, which is mainly why you don't see many 6-12 elementary schools in the UK. My sister is a teacher in the UK, and we often bounce ideas of each other. There are pros and cons for both approaches.
As PP said, it was revolutionary when it came out. But not all educational systems are as great as the British one, (I find the local schools here and in France quite Victorian), and also, not all children learn the same way.
(I am not a fan of the Steiner system, personally.)