I'm sorry, and I don't mean to be rude, but what you said is wrong, and a common misconception among those who haven't really delved into Marxist theory yet.

Central Planning isn't Marxist by itself, but Marxists want Central Planning. This is because Marxists believe Capitalism necessarily creates the conditions for central planning by competitive markets coalescing into large monopolist syndicates that already have to plan themselves. This is Scientific Socialism, a prediction of the future based on what the current direction of society is heading towards, and harnessing that via worker revolution so that these large syndicates can be gradually folded under one banner and run by a democratic government.

For Anarchists and Marxists, the State is an entirely different concept.

For Anarchists, the state is representative of enforced hierarchy, a monopoly on violence. Thus, it must be horizontal, but there can be different classes like the Petite Bourgeoisie who own their own tools or Small Handicraftsmen. Most Anarchists want abolition of classes as well, and thus usually also advocate for communes and Mutual Aid Networks with shared ownership.

For Marxists, the state is a representation of class oppression. Once classes are abolished by the folding of all of industry into the public sector, and there are no class divisions, the state is abolished in the eyes of Marxists, whithered to what Engels calls "an administration of things."

When ultimately it becomes the real representative of the whole of society, it renders itself superfluous. As soon as there is no social class to be held in subjection any longer, as soon as class domination and the struggle for individual existence based on the anarchy of production existing up to now are eliminated together with the collisions and excesses arising from them, there is nothing more to repress, nothing necessitating a special repressive force, a state. The first act in which the state really comes forward as the representative of the whole of society -- the taking possession of the means of production in the name of society -- is at the same time its last independent act as a state. The interference of the state power in social relations becomes superfluous in one sphere after another, and then dies away of itself. The government of persons is replaced by the administration of things and the direction of the processes of production. The state is not "abolished", it withers away.

I recommend reading or re-reading Socialism: Utopian and Scientific, which is the source of that passage (and explains Scientific Socialism). Hierarchy is not a problem for Marxists necessarily, but it absolutely is for Anarchists. Marxists believe that communes can result in trade, resulting in differences in material conditions and thus accumulation, starting the entire process of Capitalism anew, this is why Marxists do not want what Anarchists want, just like Anarchists don't want what they consider a state, but Marxists do not. For further reading on this critique of cooperatives from the Marxist perspective, see Engels' Anti-Dühring.

Alternatively, for a short, 20 minute article going over the same concept I just outlined but in greater detail, Marxism vs Anarchism is a good middle ground between reading the aforementioned Engels books and just my comment alone. Your sentiment is a common one, but I have yet to see such sentiment backed up by quotations from Marx and Engels that go against what I have just laid out. Normally, people who share your sentiment stop purely at the phrase "stateless, classless, moneyless society" and cease to dig in more to how Marx and Engels used those terms in their broader writing.

I am not arguing against Anarchism here, many Anarchists have tried to tackle the problem Marxists raised a long time ago and thus there are good arguments from Anarchists on how to avoid this, but the crux of the matter is that the 2 camps want what I outlined for them and believe the other to be unsustainable or unjust.

Really, I'm just a theory-nerd for Marxism, which is why I made my reading list to begin with.