The problem lies within how you yourself just framed the issue. You say “we need to feel protected from the police and ourselves.” This implies that the police are inherently separate from the rest of our society, i.e. the “thin blue line” bullshit that is one of the most malignant memes in our society today.
Police should not be held apart from the rest of society, they have a job to do just like the loggers and the delivery drivers and the teachers and the bakers and every other person who has to be held accountable to the same rules as everyone else.