Nope. Private capital allocation decisions are the foundation. It is a mistake to mix this with wishful thinking, the same flavor of mistake as claiming "socialism is about making economic decisions that reflect the will of the people rather than the will of the rich," it assumes success at the aspirational principle when that assumption is something you must avoid at all costs if you want to understand success/failure at achieving the aspirational principle. Instead, a discussion about the foundation of a system should be very carefully confined to what the system actually does: capitalism is about private capital allocation decisions, socialism is about public capital allocation decisions, and in practice everything is mixed.

Anticompetitive incentives and behavior are a natural emergent property on top of the private ownership foundation: network effects, platform effects, last mile dynamics, dumping, hell even economies of scale are intrinsically anticompetitive at the same time as they are intrinsically beneficial. Regulation to restore competition amid these natural anticompetitive tendencies can keep them in check and most people would agree this is generally a good idea -- but most people don't make the capital allocation decisions and most people don't learn about the world except through media controlled by people who do, so not only are the regulations 3 stories above the foundational principle, they are doubly insulated from effectively checking the dark forest on the second story by the very nature of the foundation itself.

You have probably heard about how misalignment emerges in socialism, because that is a story the jedi would tell you: capital allocation decisions made without skin-in-the-game accountability tend to cause malinvestment because as far as elected representatives are concerned the job is the product. Of course, a socialist government is aware of this tendency and tries to control it, just like a capitalist government is aware of anticompetitive tendencies in its own economy and tries to control them. The degree of success varies.

When there is nothing to compare against, propaganda can hide almost any mismanagement, so I am glad that we seem to be entering a second period of genuine competition. I'm less glad that this brings with it a second period of genuine "hopefully we don't kill each other / ourselves," but so it goes.