You still need price pressure on the schools. If tuition keeps on going through the roof but no one cares because it's "free" we're still blowing a lot of money that could better be spent elsewhere.
I'm not sure how it's done in Scandinavia. I think the government can simply fund public universities with a lump sump (per student), and disallow any tuition charges. Universities could then raise additional private money to use as they see fit.
In Finland the operating costs are nationally averaged to make up unit rate (google: yksikköhinta). Majority of state funding can be then traced back to Unit rate x number of students.
You will not make things more efficient by having them run by the government, you will only create another unfunded mandate. While it may seem that it is free if the government pays for it, obviously someone pays. The least cost effective way to run something is through a government bureaucracy, that should be pretty clear by now.