I took some time in thinking about your response, I want you to know that. That said, "There’s lots of places in the US where cops are paid significantly above median wages for the region as their base pay," doesn't mean much in the context of my original statement. My original statement said very much the same in fact. Cops, on paper, get paid above average and have tons of opportunity for overtime. What your response misses is the danger associated and the expectation of overtime.
It's one thing when you can have unlimited overtime and another when you are expected to take unlimited overtime. There is also a disconnect when that overtime comes with an expectation of being shot and killed. With those expectations it's no surprise that police are the largest portion of a city government. If you have a group of people that you expect to work long hours, work extra overtime, meet the municipality's needs, and potentially die in their duty, then they should command a large portion of the budget.
If you don't want to pay people to do these things then you can't be upset that they don't do those things. You get the cops that you pay for. I'll be the first to say Fuck the Police, but I'll also be the first to say we get the Police we pay for.
It's only common for government jobs and isn't universal there either. Many government jobs in the US receive multiple different types of leave concurrently. So for example you might accrue 12 hrs of vacation leave per month, 8 hrs of sick leave, and have a floating holiday of 8 hrs per year. If you reach a certain cap (say 100 hrs) the vacation leave rolls over into sick leave.
If you quit your job they have to pay out the vacation leave but not sick leave.
The result is that many government employees, with long careers, historically have tons of sick leave they aren't using (as in several hundred hours). When someone has a life event it's not uncommon for coworkers to donate some of their leave to the person (think having a baby or a cancer diagnosis).
You can of course take more leave then you have sick days with FMLA, but they will be unpaid (by your job, you may qualify for something like short term disability, idk). Sick leave that you have when you become eligible for pension retirement typically can apply to your retirement (potentially allowing you to retire earlier), but you still have to qualify for retirement first.
If you're 3 years from retiring and you can't qualify for early retirement with your leave, then you might have hundreds of hours you're not going to be able to use.