There are different “factions” and accreditation organizations in Montessori. Some are more liberal and others are authoritarian and rigid. Not all Montessori schools are like you describe, but some certainly are.
Which families tend to win the lottery to go to these schools? The parents that can afford to. Even if the school is free, the transportation is often not. Plus the parents have to have enough free time to be aware of the lottery for their 3 year old.
(disclaimer: my wife got accredited by AMI)