My friend from Finland wrote: "Yes, basic education has to be free, and private schools are heavily regulated. They need to be accepted by the government, and then they will be paid a lump sum by student, most are assigned students from nearby addresses same as any public school, and that's it. (Students can apply for other schools than the nearby one, but the nearby students have priority.) Private schools can (and do) charge for extracurricular activities, have support associations, etc; and there's the question whether the assigned lump sum should be same for all students is debated, since the student population in some schools is much more challenging. So private schools teaching mostly children from well-off native families (because of where they are situated) can do more with the same sum than schools in less prestigious areas. I found some data saying that there were 2276 public schools in 2019, and 85 private schools in 2014, so they're not very common, though about 1/3 of schools in Helsinki are private. There definitely is fear that "elite schools" are becoming more common. If urban inequality between school areas gets worse, it's very possible IMHO, but I'm not seeing it yet."
The only thing inaccurate about the image is that the nurses are too good-looking.