The US has a majority of publicly-funded primary schools (K-12)—- 16,800 districts by a recent count —- that are primarily funded by local property taxes and run by local school boards. Only 9% of schools are private, and only 7% of public schools are charter schools (semi-private).
National funding for primary education in the US is relatively small (roughly 8%) and is mostly tied to special services. The US Dept. of Education is toothless: it is primarily focused on setting policies and administering Title 9.
If Sweden has a problem with profiteering in national primary education funding, it is difficult to draw an analogy to US schools just based on the facts stated above.
It is true that some US school districts suffer from funding shortfalls due to low local tax base, and the need to show passing grades does drive some schools to “cheat” in order to receive state and federal subsidies, but this is not a universal country-wide problem.
The magic solution to educating low-income, socially disadvantaged children who live in very difficult living situations with no assistance from parents has yet to be devised. Or has it? Check out what these folks are doing in Baltimore: https://www.thread.org/