No their kids have never seen the inside of a public school. There are waiting lists in paris in the good private kindergardens and parents (as well as kids sometimes) get interviewed.
kindergardens are effectively a good route to get into good public schools if they could not secure a good public school kindergarden.
But then to pass to the public school, they will have to pass exams.
Why aren't they planning a private school from kindergarden till A-level?
because they kids will be seen as too stupid to make it in the public school system.
It is just cultural differences - behind it the idea ( false or true) of meritocracy.