An important point which I don't think has been mentioned is the ability of the public sector to retain the best staff.
Local authorities I work with spend thousands every year on attracting and retaining qualified professionals to run their statutory services. This is foe things like environmental health, planning, public health, where good staff directly impacts the quality of lives of taxpayers.
Most local authorities are banded, not meritocracies - unless vacancies come up you rely on moving up bands or annual pay rises to justify staying in your workplace. Public sector, unlike private sector workers (and i speak as someone who has experience working in both) don't get pay rises and bonuses related to company performance.
After a few years a decent qualified planner or surveyor, for example,will leave their Local authority role to work in the private sector. It will be for the money, the novelty of being being abused by members of the public, and the opportunity to progress into more senior roles far more easily.
The idea that in a time of crisis we hammer down public sector wages (in real terms) when we need the best people to help support areas, rebuild communities and bring us out of the pandemic (and Brexit) with a fighting chance seems insane.
But once again, the government do a great job a putting one group against another (public vs private) to keep us from challenging govt and demand we are all fairly paid, taxed and supported.