Just to add some details, the choice in Italy is not always completely free, because in some areas there's not that many schools easily reachable, particularly from high school upwards. The majority of students doesn't really commute until University, and even so a lot of them do it mid/short range.
This is actually less an issue than what it may seem, because the choice of high school or uni is mostly based on what one wants to do (or is forced to do!) and much less on the alleged "quality" of the institutes. So the typical choice is between the closest technical school or the closest gymi, not between two technical schools based on their rankings.
There are of course private schools, mostly associated with church, and private unis, but they don't necessarily provide better quality (to be generous...).
There are also schools with very bad reputation but they are mostly associated with their education level - you won't find a disaster gymi, while you could easily find two bad professional schools in the same area, because that's where problematic youngs go (sorry to say, it's probably a whole separate discussion).
Overall I always went to public schools, from kindergarten to PhD, and the close-by offer was always of good/high quality.
Maybe sometimes, but it's also a source of income for kindergartens where offer is X and local demand is Y < X...
However starting from regular school (age 6) this is rarely an issue, class composition is more flexible and there is rarely the need to exclude anyone. Non-existing in high school... in my gymi the number of classes could vary from 6 to 13 each year depending on the number of subscriptions, each class with 20 to 30 students.
Of course the extra classes will get temporary teachers, most of them move yearly or monthly and don't have a permanent contract, this has an obvious impact on quality but somehow they often manage to stay "above threshold".