As with all sectors of the public service, there are some people who earn a small fortune for doing very little work. These people are the exception and not the rule. I have worked in the public sector (in both local Government and the Police) and I now work in the private sector.
The idea that your rank-and-file police officers are earning big money is erroneous. I was a police officer for several years in Greater Manchester Police and I can assure you that 'overtime' is a dirty word – myself and my colleagues regularly worked 11 and 12 hour shifts (normal shift is 10 hours without any real break) and I never got a sniff of overtime. We were lucky if we got to take the time off on lieu by finishing a shift early – but this happened so rarely that after a while, you stopped bothering to make a note of the time you were owed and just accepted it as part of your job.
Having worked in both the public and private sectors for many years, I honestly believe that they are very similar. Both contain some people who are grossly overpaid for what they actually do but for the most part, they are populated by hard working, conscientious people whose salaries tend to reflect their roles and responsibilities.