The key disconnect is that the state itself is a product of the base of society. Marxists do not posit that we should merely merge with existing government and take it over, but smash the state apparatus and replace it outright. The capitalist systems of today, despite having a public sector, are entirely controlled by capitalists. The socialist states of today and the future, despite having private sectors, are thoroughly controlled by workers. Look at Cuba, and what it's able to achieve despite incredible blockade and sanctions. Look at China, where the underdeveloped parts are marketized and the developed parts are public, they even have a handy chart on what socialist construction looks like:

This is where philosophy comes in. Right now, your analysis is metaphysical. You see that in the past the market was more decentralized, and now that it is highly decentralized, you are trying to work backwards. This isn't how human societies progress, though. This new economic base that capitalism has created is already compatible with planned, social ownership. There is no such thing as a static system that is not evolving into something.

Dialectics helps us understand that capitalism has already played its progressive role, and that now it's time for workers, who already run the world, to take charge of it and own it. Marxism is a more scientific way of viewing the world than liberalism allows for, because metaphysics traps us in outdated forms of science, just like evolution proved older, metaphysical forms of biological categorization to be incorrect.