As the question is asking about the "Scandinavian" model, I will try to provide an answer from a (central-)European focus.
During the Middle Ages universities, as we know them today, did not exist.
The universities from those times were often independent study and teaching associations without formal structure.
During the Renaissance, alternative research circles formed outside of the universities.
In the early modern age (Napoleonic and Victorian eras), many things changed.
For one, the idea of nation states emerged.
This meant that the administrative cadre was no longer simply nobles who fulfilled their duties to their overlords, but that there existed a state who employed people as administrators.
This coincided with the rise of a Burgeois class of administrators, who needed formal education to fulfill their duties. This led to state run primary and secondary eduction, but also to the establishment of "modern" universities. For example, France instituted universities (or "grande école") that educated their students in one particular topic (such as naval engineering or mine supervision). In Germany, for another example, the Prussian reforms after the defeat against Napoleon established a similar bourgeois body of administration instead of the absolutistic system. University were founded to guarantee proper eductation to the new administrative cadre.
These early universities were seen as necessity by the state to raise its own prospective administrators and were therefore largely subsidized or run by the state itself.
However, Humboldt developed a different vision.
Among other things, students at this university should have the freedom of study, rather than following a strict curriculum.
His ideas spread throughout Europe and even into the United States.
The modern European university system is therefore a remnat of these Humboldtian ideals.
The state no longer funds universities for creating their own administrative cadre, but to offer a comprehensive education for its well-informed citizen.
The question about the socio-economic benefits therefore becomes a bit moot, as the states run universities not because it is cheaper (or better) than private funding, but because it is seen as the duty of the state to provide this type of education.
Of course modern systems vary quiet widely between countries (even in Europe), so that of course there exist many nuances that I did not cover in this answer.