Replace 'police' for 'people' and we find out that no one can ever be held accountable.

"The police" is not a single body, there are multiple police forces which are mostly independent. I don't know the US system very well, but at least where I live the cops that work on the street have a completely different chain of command than the detectives who investigate them if necessary.

When you substitute "people" for police, you're missing a crucial ingredient; other police officers have an institutional alignment with their fellow officers, and will continue to interact with other officers. Further, they are likely to need to be able to "get along" politically with other police departments in the future even if they don't interact with particular people in those departments day-to-day.

On the other side of the scale, the relationship with the mistreated citizen is totally expendable, and the relationship with the public consciousness is a diffuse one rather than a concentrated one (i.e. there's no one-on-one rapport with individual citizens, only a generalized "police force" and "citizens at large" relationship).

Game theory reliably predicts the outcome here: the diffuse and expendable relationships are likely to take a back seat to the concentrated and durable ones. Obviously this doesn't predict individual outcomes with certainty, but the imbalanced incentives with intra-institutional review are pretty significant.

"citizens at large"

I listen to the local police radio on the internet (it's oddly relaxing), and they have two terms for us: suspects, and reporting persons (RPs).

Your comment seems to imply police are never punished for misconduct and yet that is obviously not true. Internal Affairs is a very real thing.

Yes, they do get punished, but they get away with enough that they deserve their reputation.