As a counter example, the OECD PISA ranking for education puts Estonia as just barely ahead of Finland[1]. Estonia has public and private schools[2]. So, it is at least possible to have Finland quality schools while maintaining a public and private system.
Another thing to consider would be the population differences. The US has ~65 times more people than Finland. In this larger group of people there will be Finland sized subgroups that outperform and underperform Finland even though the US as a whole underperforms.
Massachusetts, for example, one of two states in the US to perform and report their own PISA numbers, is pretty comparable to Finland in 2015 (1 or 2 points above or below on scores of ~500 for science and reading and 11 points below on math)[3]. I couldn't find the official OECD results for 2018, but I believe Massachusetts is slightly ahead by then.
1 - https://www.oecdbetterlifeindex.org/topics/education/
2 - https://en.wikipedia.org/wiki/Education_in_Estonia
3 - https://www.oecd.org/pisa/PISA-2015-United-States-MA.pdf