If you look throughout history, you'll see that before the advent of what we'd call 'modern states', most people who got their paycheck from 'taxpayers' did not see themselves as working for said 'taxpayers'.

Example: Pharaonic Egypt. Alexander's Empire, Bourbon France, Tsarist Russia, or more generally any kingdom, empire or any sort of duchy/earldom/county/etc where you have someone (the King, Tsar, Emperor, Duke, etc), whose job it is to lord over the peasants and take a cut of their work, not because they are an elected public servant doing the will of The People, but because they believe God Almighty has decreed that living off the wealth of others, and occasionally wasting large amounts of that wealth on building palaces or waging costly wars is what they were born to do.

https://en.wikipedia.org/wiki/Divine_right_of_kings

as such, if you view the modern state as "basically an oligarchy masquerading as a democracy", then the police are not in fact working for 'Joe Taxpayer', but are just playing the same role that medival knights played for the Kings of France - they are the armed force of the extractive state, whose job it is to keep the peasants in line via violence so that they can continue to live off the fruits of peasant labor.