I agree with much of the rest of your comment, and in the past I would have agreed with this as well. However, police are not inherent to the human condition. (We haven't always had police, and with luck we'll be rid of them soonish.) When police were created, it was largely for basically racist purposes, even if the "races" under consideration in many locales were "Irish" and "Italian". (Further south, however...) People would have objected to a police force imposed on everyone, so the trick was to impose it mostly on those who didn't control the public purse or the courts.

A society that relies on relentless, capricious violence to compel large swathes of the population to accept their assigned roles is not pareto-optimal. We will improve when we change our laws with the goal of reducing the necessity of policing.

Ok, but I think this is a reflection of different races falling en masse into different social classes. If you're in Italy and your city has natives, gypsies, african laborers, jews, and persian merchants (note: stylized example, not necessarily reflective of any historical events), I'd expect the police might be called into being as a defense (or, depending on your perspective, offense) against the gypsies and africans, while at the same time people largely didn't care about the jews and persians (from a policing perspective). They'd be dealt with more by the taxing authorities.

If the police were an expression of racism, I'd expect something different.

But think it through further, please. Why do different races fall into different classes? There is more than one reason! For your average racist fuck, the answer is "because race". But TPTB are not all, nor even primarily, average racist fucks. Like "race", "class" is an invention that allows elites to control and extract rent from the rest of us. Classes seem to the average person to be more contingent categories than races, so the concept of race is used to bolster that of class. It's easier to convince a poor white dude to oppress poor black dudes than it would be to convince him to oppress poor dudes in general.

Also, don't expect policing to conform to reasoned expectations. It is more effective for its real purpose of controlling and extracting rent from the rest of society, because it is capricious and unpredictable.

You argued (as I understand things) that the motivation for forming the police was usually "racist", and that it made more sense to view the depredations of police as race issue than a class issue.

I counter that in a society of several racial groups, some poor and some wealthy, I think the police would be expected to spend their energies on the poor groups while leaving the wealthy ones alone. To me, this is evidence that the police are a social-class based instrument rather than a race-based instrument, because if they were an expression of racism they'd be expected to spend their energies on aliens while leaving natives alone (in this analysis, Jews who have been resident for centuries but maintain their own separate culture are "aliens", not "natives").

You say that the different treatment of racial groups according to what social class they belong to is just more racism. You can call it that, but the label stops being useful -- if the police are a "racist" institution, by this definition, you can't predict anything about how they'll treat someone even knowing the race of that person, or knowing whether their race differs from the race of the police they're interacting with, or whether it differs from the race of the group running the police, or any such thing. You have to know their race and the position their race occupies in society. But the social position is doing all the work -- your predictions will be nearly as good if all you know is the personal social standing of the person interacting with the police. Race is a sideshow.

Why is treating different races differently because they have very different social standing primarily an issue of race rather than social standing?

Your example seems to be a largely static one, which is neither realistic nor particularly illuminating. Policing like any "modern" phenomenon is relatively recent, so we should examine the entire narrative of effects rather than taking a snapshot and presuming it to encompass the whole range of possible experience.

Race admits to much less mobility than most other pretexts for oppression. That is bad because it makes society less agile, and because it kills hope and confidence. Both of those emotions are entirely beneficial, so their loss in any subgroup is harmful.