In countries where universities are free or almost free, there are limited spots, and few people can actually get that free education.
There is some misconception that education is available for free to everyone. That is false. Education is free but available to only few. There is usually some entrance exam system to determine who gets to study and who is just left out
Since you mention Italy, you can check on:
http://ec.europa.eu/eurostat/statist...2016_(%25).png
Only 19.4% of Italy have higher education. The worst educated country in all 1st world countries. While in the U.S. that is like 40% or more, and one of the best countries in higher education percentage of population
can also check https://en.wikipedia.org/wiki/List_o...ion_attainment if you want more countries
tl;dr I don't think Italy is good example for education. It is the worst in western world.
I don't have info about the healthcare you mentioned, so I don't know how well Italy fares on healthcare