Appointments are a whole other issue (see the extreme turnover in the American executive branch every 4 years). Id rather the head of my local police dept be significantly supported by the populating instead of an appointment from a governor, mayor, ... whose entire schtick can change on a dime.

Independent elections are a good thing. Bundling offices together under a single election that appoints the rest of the world is terrible and only leans further into the two party see-saw that exists in the USA.

I really wish for proportional representation. Not that it really applies to your local police force, but we need to break apart the complete A-or-B nature of American politics. Form coalitions, not monoliths that trade off earning 51% of the electorate every cycle that the completely repoints the entirety of the govt for the next 4 years.

On the other hand, look at our current appointed DoJ and FBI leadership. No solution is foolproof.

In larger counties, the elected Sherrif is usually more managerial and less hands on. If not elected directly, the Sherrif would likely be chosen by the elected County Board of Supervisors. Which I guess gives you more ability to fire, but also means more indirection from the will of the people.

Nobody was pressing (or even alleging) crimes by the sheriff AFAIK.