However, the governments are playing with the idea of not keeping public salaries with inflation.
Are you talking about a particular government or in general? I think that any government that wants to be re-elected (in a democratic world) can't turn its head away from inflation and not adjust salaries, because that's how they would shoot themselves in the leg - people feel on their skin very quickly if their standard of living deteriorates. Opposition forces will certainly use this to their advantage before the next elections.
Depending on the country and the flexibility, this means that civil servants and public sector may become underpaid and those who actually have skills may leave to the private sector. As a result, I forecast that public services are going to deteriorate.
We can again talk about the public sector in general, but its quality is not only determined by how much someone is paid, but also by the abilities and competencies of the people who work in that sector. For example, I will give you the example of my country, which is a member of the EU - but it is extremely corrupt and the chances of getting a job in public administration are almost zero if you are not a member of the ruling party. The people who work there are politically eligible, but far from being able to do their job properly - the judiciary is in such poor condition that the average trial takes about 10 years.