I am not entirely sure what you are asking.
The first part says we can look at society and see various organizations, and understand that they affect the actors in them and who relate to them – people who fill the roles they offer – etc. Okay, I agree.
Then, I think you are asking, why bother going another step? Why look at that a bunch, and discover, say, that there are owners, coordinators, and workers – or women and men, or different races, or disabled and abled, or tall and short, or whatever else you might want to highlight and give a name? The answer is, you would to it to focus attention and to ease communication, and not have to start from scratch over and over – on the one hand, and in the case we are talking about, to identify group actors, not just lone individual ones.
A physicist could say we look at the clash and jangle of tiny little entities in context of certain relationships that always hold – conservation laws, etc. True. Now why go on and name the entities – electron, photon, quark, gluon, and so on… Well, the reason, again, is that we see these similarities among some of the entities, and we find it is useful to be able to talk about all of a type, and is critical to pay attention to the relations of one type, and other types, and so on.
A biologist identifies in the complex mass that is humans, but then examines further and sees lungs, heart, kidney, even circulatory system, say, and gives each a name. This is to allow amassing information about each, and their relations, to easily communicate about it all, etc. But the biologist does not give a name to the combination of wrist and knee. Each alone, yes, but not the two, together. Vein and capillary alone, but also together, and with much else, called the circulatory system. The reason is purely a matter of purpose. There is a massive complex whole – and looking at it at the first level you indicate, we tease out aspects, give them a name (that’s a concept) and then, having done so, we pay close attention to what we are highlighting and we can easily discuss and develop related claims, communicate quickly about them, and so on.
Okay, back to society. Some think we should highlight economic institutions and then key constituencies (classes) that our examination of those institutions reveals. Why? Because, they must believe, paying close attention to them and their relations and dynamics (as compared to paying close attention to red heads or people who are left handed, or who are over six foot 5) makes sense and indeed is critical for purposes of acting to change society. Someone else might say, well, yes, but I think culture is also central and or polity and gender, and here is why I believe that, and in light of that, why I tease out, from the whole, other elements than just economic ones to pay close attention to.
Now, does it matter? Well, here is but one example. Everyone who forms a workplace coop may well agree with you and feel they practice what you outline at the outset. They may even go a step further, and identify owners and workers. So they know they should have no owner and be non profit because they have analyzed institutions far enough to have that in their set of beliefs. But suppose they do not identify the coordinator class, it just isn’t a concept for them – they haven’t pinned a name on it, and analyzed the relations it has, and so on, and they do not have as part of their understanding that it arises from a corporate division of labor, and so they don’t decide to get rid of that, but instead they preserve it. Around the block a different bunch of workers, does have that concept, does have that understanding, and so institutes balanced job complexes constituting a new division of labor. Clearly, this matters.
On a larger scale, a movement for ending poverty forms and develops a program. One decides to appeal to owners – they have the most power and wealth. Another decide to appeal to the coordinator class types. A third decides to appeal to working class folks, and to pressure the other groups. Very different.
One movement says race and gender evidently concern people, but our concepts say they are just ancillary to race and to be efficient and effective we should understand them simply in relation to their effects on class unity, etc. etc. Others instead, conceptualize these and highlight aspects and so understand them in their own right, as well as in interconnection.
OF course in a classless economy – an economy that has institutions which, whatever else they do, they do not generate classes and class rule – there can be other problems. Class analysis per se doesn’t deny that. What would deny that is a mindless – in my view – stance that says the economy causes all that matters, and a classless economy therefore leads to good in all respects, inexorably.
You could have, for example, a classless economy in which ignorance of greenhouse effects leads to choices that doom humanity…at the extreme. Or one in which women are treated as subhuman, say.
So the interplay of institutions approach you identify we can call top level, if you like. Then, however, we use it – wanting to see how society works in order to be better able to change it in directions we desire. So we do that and we learn things, and it turns out one thing we learn is that certain groups of people play a big role in historical trends, so we identify them and try to understand them, and then, if important, and it is, we add the new insights to our conceptual toolbox, if you will.
Can ripping off other countries lead to some benefit not only for the very rich and powerful, but even for others in an imperial country? Yes. Sure. But not relative to having a better economy.
Suppose the mafia runs your neighborhood. They give some very modest benefits to some subset of the population, but keep must of their plunder, themselves, of course. They create a climate of hate and fear. They block all kinds of beneficial approaches, and so on. Now, did the subset that got some fruits of their violence get that? Yes. Did they on balance benefit compared to a better situation, no? But additionally, should someone getting some benefit from the ravaging of others be appealed to first and foremost on the grounds that they could do better, some other way? Not really. I think their horrendous moral stance ought to, albeit carefully.
But now consider another possibility. Take England’s relation to India. At the height of that colonial/imperial relation, some estimate that England spent two billion a year on maintaining the subservience of India, and remitted back to England only one billion. BUT – the two billion came from the general population, in taxes. The one billion went to elites, owners, etc. This extreme case is the more general situation. The population pays diverse costs that allow elites to rip off other countries – the broad population not only doesn’t benefit, it loses.