Its hard for me to imagine people ever wanting a corporation to openly replace the government, and I can't see why a corporation would want to do it when in most places today they can already achieve the same results through bribery, government contracts, and control over regulations. Although, I like that corporation states serve as a metaphor for our relationship to modern day global corporations. They look and act different, but the effects seem similar.
It felt like a complete corporate state sounded similar to authoritarian non-democratic socialism, where the state centrally owns all corporations below it and a very small elite profit off of an abused working class, as in North Korea, or maybe a fascist dictatorship where lower classes of workers are abused by state corporations to enrich both the elites and an innately priviliged group of society.
The same things seem to happen in different ways in the USA, even though it is not authoritarian socialist or fascist, and not a corporate state. The elite are still whoever owns and controls the conglomerates, but instead of the elite controling the government directly, they control through bribery, extortion, and proxy "non-profit" organizations. Three corporations which both hold influence over the government and are heavily influenced by the government control the majority of the news we see, corporations routinely block welfare or public infrastructure while negotiating generous taxpayer subsidies, and race based segregation and discrimination against racial minorities and LGBTQ people is common.