Italy here.

It’s great to have it, and as I see what happens around the world I understand how nearly utopian-like the concept is.

… but people will complain and moan about it anyway, and the main reason is that:

• while being universal every different region (20 in italy) has its own locally administered and budgeted subsystem implementation which might will differ from the next region system and so patients data won’t be able to be transferable or even observable from each different region network
  Also the level of cures you receive might vary in their quality from region to region

• it is understaffed because the salary is not worth the responsibilities, unless you get to be a specialist doctor, so for instance there are not nearly enough nurses or sometimes triage doctors, and so many workers have to go through extenuating working hours scheduling to cover for that, and of course this will affect their performance and even sending some into burnout

• it is understaffed because it is under budgeted and this is by design bay politics, ultimately run by right-wingers since some decades already, who are trying to give the people more and more reason to hate the public health system, so one day they might be able to succeed to sell all the public (paid with peoples taxes) infrastructures to privates, transforming the public health system into the “american dream” health system

• it is under budgeted because taxes here are paid for the 70% of the total by employees and by retired people, which constitutes but a glimpse of the personal profits of the total, while every one with an autonomous job, including companies, just fuck with taxes, year after year, in a systematic and systemic way, so much that every new government will indict a new taxation amnesty because the budget needed to go after the unpaid taxation is more than the taxation not earned.
  …o yeah and after that the same politician will complain and moan about the public health system being inefficient and needing a privatization reform.