More to the point, does it increase participation of poor people in the best universities and the best (as reflected in higher salaries) degree programmes?
The Italian experience is that free universities were (are) routinely oversubscribed. They opened loads of new universities in poorer areas, and still were eventually forced to introduce limits with entrance exams. The most in-demand institutions eventually reintroduced fees, although much lower than UK or US rates (we are talking 100/200 euro per month, tops). So I'd say the answer is yes.
In fact, Italy has now the opposite problem: there are too many graduates and not enough jobs, so highly-educated people (especially from poorer backgrounds, i.e. lacking long-standing social connections) are now moving abroad in very high numbers.
How many graduates in Political Sciences and Literature are there ?
How many job openings that require this specific knowledge ?
Most of my collegues graduating with me in Electronics were working in Italy within weeks/months of graduation.
But I generally agree that being available to everybody the degree in Italy is somewhat devalued.
I'm not saying degrees are "devalued" (European opportunities abound, after all, and most Italian graduates are actually very smart), but it illustrates that making education (almost) free will always result in growing numbers of graduates from all backgrounds. This is a good thing overall IMHO, but should be expected and planned for.
Correlation does not imply causation. In Spain, jobs that did not require a university degree were paying really well before the crisis, so many people were joining the labor force at a young age instead of going to university. From my observations, this was specially prevalent among people that came from less educated families. Suppose that at the same time university fees were going up (I'm not sure about this). In that scenario, if you looked at the data, you could wrongly conclude that rising tuition fees were discouraging people with less educated backgrounds from attending university.