Unlike the communistic system where the political leaders use the system to enrich themselves

Historically untrue of many communist leaders. Ho Chi Minh mended his own clothes. Vladimir Lenin was practically ascetic.

Obviously both are purely economic ideas that can’t exist in their ideologicsl [sic] state in reality.

Capitalism is an economic system that produces commodities: goods that are made to be useful but can not be used until they are bought/sold. Under capitalism, the capitalist owns the means with which to produce commodities and so takes the finished products and ultimately the resulting profits as their private property. The capitalist also makes all the decisions on how workers spend their labor time. On the other hand, the workers, the people that labored to create the commodity, are given a fraction of the value they produce in the form of wages. Capitalism exists here and now, any definition of capitalism to the contrary is idealist.

It’s fair to say that capitalism scales better than communism.

We have examples of socialist states scaling just fine. Perhaps we could have seen the true potential of socialism (and eventually communism) as an economic model; but countries that reject capitalism faced economic sanctions, diplomatic isolation, assassination attempts, and retaliatory wars (e.g., Cuba, Vietnam, USSR, Chile [Salvador Allende], etc.)

Private ownership according to your contribution works very well in the realm of society.

You can keep your house and toothbrush under socialism: this is your personal property. The goal of socialism is to turn the private ownership of the means to produce all the things we want/need into public property that the workers own. This is necessary for us to stop producing goods for private profit and start producing them for direct consumption.