While this criteria exists in all systems, it is the most defining one in communism and other authoritarian systems.
Update: parent comment was substantially changed since my comment was written. It originally said something to the effect of: 'but true socialism has never been implemented'. Perhaps I should have quoted it to avoid this confusion/deception.
Socialism isn't about state control, the socialist states that existed (and still do sort of exist, notably Cuba) see themselves as transitionary states between capitalism and socialism, up until the time they're no longer necessary (I don't defend this approach, there's multiple reasons why I believe this is wrong). These states never claimed to be practicing socialism, but they remain socialist states because of their end goal.
If you're interested in stronger well structured arguments for socialism, from an anti-authoritarian perspective I recommend reading the writings of Bakunin and Proudhon for more theoretical looks at property and the state. Kropotkin is great for anarcho-communism. Here's some books I recommend with free links:
The Conquest of Bread by Peter Kropotkin (Check this one out first) https://theanarchistlibrary.org/library/petr-kropotkin-the-c...
What is Communist Anarchism? (Or this one first, they're both great intros) By Alexander Berkman https://theanarchistlibrary.org/library/alexander-berkman-wh...
Anarchism and Other Essays by Emma Goldman https://theanarchistlibrary.org/library/emma-goldman-anarchi...
Mutual Aid: A Factor of Evolution by Peter Kropotkin https://theanarchistlibrary.org/library/petr-kropotkin-mutua...
And not particularly an ideology book, but an interesting firsthand recount by George Orwell of his time fighting with Socialists and Anarchists against the Fascists in the Spanish Civil War which is called "Homage to Catalonia"