I’m by no means an expert on education but no article I’ve ever read explicitly links the success of the Finnish school system with banning privatised schools.
The most quoted reasons for its success are:
1) Non-competition between schools (rankings)
2) Non-standardised testing
3) More playtime and no tests for kids.
4) Very little homework
5) Well paid, well respected, well educated teachers
And those changes happened in a 40 year period, not in a flash. You can always make great changes to the current system without leaping straight into seazing of private assets like it’s a natural reflex. It shows other underlying intents rather than fixing things.
Also bear in mind that Finnish society is very different from ours. Far less urbanised and far more homogeneous. Many inner city schools here are a mess because of how our society overall is structured. Fix that before forcing parents to send their kids there.
Inb4 some claim I blame the immigrants or poor people (the literal victims of the current state) for the failings of inner city schools.
If you haven't read an article that links the equitable nature of the Finnish school system to its success... I can only assume you haven't read very much about it if I am honest. I am not saying there aren't other factors like the ones you've just mentioned. Although it does amuse me that you have just listed what you call "the most quoted reasons". Where do you get that stat from? I'd like to see the data on 'the most quoted reasons for the success of the Finnish school system'... unless you've just made that up?
I don't have a particularly strong view on the abolishment of private schools if I am honest. I do think something more drastic like that will need to be done though if we are serious about really wanting to close the attainment gap and create a more level playing field for children where ability and not wealth is the main driver of attainment. Just taxing private schools a bit more won't change the fact that many top professions go to an extremely disproportionate number of the privately educated.
Also, I suspect the school standards across the board in this country would likely improve if a lot of the very wealthy people in power had to send their kids to the same schools as everybody else.