Any interest in returning to this conversation? I'm involved in abolitionist organizing in Arkansas, USA, but after recently reading The State and Revolution, I've gotten kinda shaken about this very question posed by @mambabasa@slrpnk.net. I will write a bit below about some of the important take-aways from this text, but in the case of tl;dr I guess what I'm especially interested in is this conversation that Robin D.G. Kelly encourages. Could you drop some links to where Kelly says this, whether that's in these comments or in their own posts? Looking forward to it :) -Clairexo

In The State and Revolution, the key points about policing are made by way of Engels and Marx, quoting from The Origin of the Family, Private Property and the State:

But in order that these antagonisms, these classes with conflicting economic interests, might not consume themselves and society in fruitless struggle, it became necessary to have a power, seemingly standing above society, that would alleviate the conflict and keep it within the bounds of 'order'; and this power, arisen out of society but placing itself above it, and alienating itself more and more from it, is the state."

The modern state has two distinguishing features: dividing its subjects according to territory, and establishing a public power. Regarding the latter:

The second distinguishing feature is the establishment of a public power which no longer directly coincides with the population organizing itself as an armed force. This special, public power is necessary because a self-acting armed organization of the population has become impossible since the split into classes.... This public power exists in every state; it consists not merely of armed men but also of material adjuncts, prisons, and institutions of coercion of all kinds, of which gentile [clan] society knew nothing...." “It [the public power] grows stronger, however, in proportion as class antagonisms within the state become more acute, and as adjacent states become larger and more populous. We have only to look at our present-day Europe, where class struggle and rivalry in conquest have tuned up the public power to such a pitch that it threatens to swallow the whole of society and even the state."

As @Five@slrpnk.net noted, prisons aren't unique to capitalist societies; they are necessary to any authoritarian system. An authoritarian system requires prisons and policing in order to manage political dissent. A capitalist system, to whatever degree it's clearly authoritative, requires prisons and policing in order to maintain some form of equilibrium amid the inherent antagonism between classes. Since I've just recently begun studying Marxism, I'm partial to the argument that capitalism's end comes through a workers' revolution, and that the revolutionaries will require systems of force such as an army in order to engage in self-defense lest the bourgeoisie regain power. I'm open-minded about this, I just haven't yet had any conversations with people who are both serious about PIC abolition and informed in the basic theories of political economy underlying Marxism.