Regardless of whether you think it is moral to abolish private educational institutions, there's good reason to look at other aspects of the Finnish education model rather than this one single point.
Finland does not use multiple choice exams and has literacy standards that are clear and simple. Contrast this to the U.S. model, where literacy standards are a byzantine mess, and are often completely disconnected from a student's inability to read and write.
Mike Schmoker has addressed this in his excellent book Focus, where he writes:
"[Finnish] success, according to observers, is a result of how much time students spend actually reading during the school day. They found one Finnish student who, upon returning from a year in U.S. schools, had to repeat an entire grade. This is because in the United States, instead of reading and writing, she and her fellow students spent their time preparing for multiple-choice tests or working on "projects" where students were instructed to do things like "glue this to this poster for an hour"..."
I teach in a charter school. We have mandated standards requiring us to assign students X numbers of hours of reading/writing per semester. Students who leave our school and then re-enroll in later years are often entire grades behind, and have often not been assigned any writing or reading of any kind during their time in the "mainstream" public school district.
I suppose my argument isn't so much that private schools are/aren't a good and moral thing, but rather that there are many far less controversial methods of improving the U.S. school system than abolishing private education.