A country is not a homogenous bloc. Bourgeois theory accepts that views will differ within a country. This is a given. It's not what Marxists mean when they challenge the view that a state is a homogenous bloc.

Marxists go further. A country is a combination of classes, whose material interests are fundamentally opposed. The ruling class (the bourgeoisie) wants one thing. The ruled class(es) (mainly the proletariat in most modern states) wants another thing. So when Marxists refer to a state, they tend to mean the ruling class within that state. They don't mean everyone who lives in the state.

Yogthos wrote:

It's absolutely unthinkable for any western country to integrate aspects of Marxism into the system.

I believe Yogthos was referring to decisions and policies of the ruling class. If this class doesn't like something, it can legislate against it and enforce that legislation through what Althusser calls repressive and ideological state apparatuses. The ruling class is not all powerful and it does require some buy-in from the workers.

The ruled class clearly has some room to maneuver, as you rightly pointed out. Similarly, these workers can establish, join, and organise in trade unions. Co-ops, though, as with trade unions, can only be lawful if they operate within the rules of and created by the bourgeois state, which are created to achieve what the ruling, bourgeois class wants, and have a dialectical relationship to there logic of capital. (Incidentally, this is why Marxists don't care much whether the red or blue party is in power – they're both still capitalist.)

Co-ops, again as with trade unions, may even be set up by or otherwise involve Marxists. They may well be an improvement on the ordinary way of working for private companies. But two problems arise.

First, co-ops must work within the logic of capital. Otherwise, within a bourgeois state, there will be two consequences: (i) they will be run out of business by capitalists who can e.g. suppress wages and use the savings to undercut the co-op; or (ii) if they threaten the logic of capital or the institution of private property, the state will crush them.

Working within this logic, the co-op can only do so much, falling far short of any revolutionary goals. Two aspects unfold. One, the co-op is likely shown to be a spontaneous movement. Two, the co-op, like trade unions, can lobby for some reforms, but these are limited to economic reforms and will rarely be political, or political economic.

This leads smoothly into the second problem. Before stating the second problem, it must be noted that co-ops, like trade unions, could provide an structure that survives the dissolution of the bourgeois state, unlike fully for-profit corporations. And I'm not saying that I dislike co-ops; I'm saying they do not (generally) introduce Marxism into a bourgeois state.

Second, then, cooperative movements, again much like trade unions, cannot develop revolutionary consciousness (because they are spontaneous, apolitical, and they must accept and work within the logic of capital from the beginning).

Something Lenin said of trade unions seems to apply here (footnote omitted) (https://www.marxists.org/archive/lenin/works/1901/witbd/ii.htm):

The history of all countries shows that the working class, exclusively by its own effort, is able to develop only trade union consciousness, i.e., the conviction that it is necessary to combine in unions, fight the employers, and strive to compel the government to pass necessary labour legislation, etc.[…] The theory of socialism, however, grew out of the philosophic, historical, and economic theories elaborated by educated representatives of the propertied classes, by intellectuals. By their social status the founders of modern scientific socialism, Marx and Engels, themselves belonged to the bourgeois intelligentsia. In the very same way, in Russia, the theoretical doctrine of [revolutionary] Social-Democracy arose altogether independently of the spontaneous growth of the working-class movement; it arose as a natural and inevitable outcome of the development of thought among the revolutionary socialist intelligentsia.

Note that when Lenin says 'social democracy', etc, he's not using it in the way that people use it today to refer to liberal democracy. The labels have changed over time. He's talking about the revolutionary socialists.

In sum, co-ops do not introduce Marxism into a bourgeois state. Co-ops cannot take workers any closer to revolution. Indeed, they may undermine revolution, by raising those who would be in the proletariat into the ranks of the petite bourgeoisie.

Additionally, co-ops simply try to capture some of the market/capital currently held by ordinary for-profit enterprises. And as the world is already capitalist, the co-op must enter relations with the bourgeoisie to acquire resources, to distribute it's goods and services, etc.

This is why co-ops do not represent a micro-system of workers owning the means of production. The co-op is more like a spontaneous organisation of trade unionists who simply cut out the middleman.

If you want to know more about the Marxist theory of the state, you might want to look at Marx and Engels' Communist Manifesto and Lenin's State and Revolution. The former is quite short and straightforward. Both texts explain some of what I said above in more detail.

Edit: here's a good article that responds to your point about workers being granted shares (which does the opposite of integrating some Marxism into the bourgeois system): https://en.rnp-f.org/2018/09/29/exploitation-of-workers-by-the-workers/#top.