volveré y seré millones
Theoretically that should be fine since the public sector more or less takes care of necessities. The less money there is, the bigger the proportion that should be in public hands. But what seems to be the problem in what you describe is that the public sector appears to restrict its benefits, like a select club, a cozier clearing in a harsh neoliberal jungle.
Austerity actually hit the public sector the least. The cumulative losses in the private sector have been much greater in magnitude. One example to rule them all: none has been fired in the public sector, yet, vs 1.500.000 new unemployed in the private sector. How's that for "specific targeting"?
In Latin America there's a key debate about the autonomy of the security forces. Years of dictatorships and outside meddling have left police forces and military forces that more or less run themselves but can collude with other interest groups, with some politicians more or less allowing them to do that, while others have specific programs or measures to fight this issue, which erodes democracy and people's rights. Essentially, a struggle against police corporatism. It really also occurs in the judicial system on the whole when there is no way to impose the will of voters on it, functioning like a nondemocratic power within the democratic State, like a bunch of self-organizing "wise old men" that aren't really accountable to the general population, generally cloaked by the ideal of "independent judiciary".
Also, a policeman is always a public servant.
One important role of the State is to guarantee a floor for salaries and ensure salaries are reasonable, so you can't just have the private sector deciding what to pay people. You'll need at least strong unions in most sectors so workers can fight for their interests, unemployment benefits, and if you can't ensure widespread formal jobs, you need assistance for all the people who are hired without basic benefits and minimal pay.
IMO, they should not just cut them by an arbitrary amount, but align them to the average wage for the private sector.
We used to have that shit here, but the State took over pensions again, fortunately. That improved retirement payments for most people considerably and was a great step because part of the money can be used to finance long term social investment and support, not just retirement or disability pensions while private companies take a chunk of the the money elsewhere or away from the general population.
While they're at it, they should abolish mandatory social security/pension contributions or at least give full freedom to choose/move between insurance/pension companies (with laws MANDATING that the contributed sum stays intact when switching), kinda like when switching between banks. It should be the job of the insurance companies (even if state-run or state-endorsed) to offer competitive enough offers to keep their customers from bailing boat, and not forcing them to stay due to laws or red tape which make it hard to "leave the club" (also because while wages were cut, contributions did not...)