Politicians are part of the state, which is shaped by the economic system which, in most of the world, is currently capitalism.

The root of the problem is class society and the capitalist system where the ruling class are the capitalists. So it doesn't really matter who the politicians are until the economic system, and thus the ruling class, are changed, which can only happen by organizing outside the capitalist political system whose only purpose is to protect capital.

The state is part of the superstructure that is shaped by the economic base, which is in turned maintained by said superstructure. However, changes in the superstructure are never transformative unless they also come with radical change to the mode of production. Billionaires, and the capitalist class as a whole, completely block the path for the workers to seize the means and reshape society towards progress. It doesn't matter what faffing idiot you put in power in the state, when the economic base keeps operating with the same logic of capitalist extraction.

Many middlemen are getting played, too.

You forgot the journalists who frame narratives and the intellectuals who secrete the ideology that makes it all possible.