There is so much wrong here I don't even know where to start. But it did give me a good laugh this morning. So I'll take a crack at it.

Lets go through the ideals

"No private property" - can't have an economy without private property.
"No profits off the labor of another" - this is nonsense.
"All people are equal" - no they are certainly not. Only equal in rights, nothing else.

The part about personal and private property is just plain silly. You either own something or you don't. Beyond that it is an attempt to justify communist bullshit by playing with definitions.

"If this is taken away from the proletariat (the working class), the resulting system is not communism." - this is right down amusing. If communism fails miserably then it is not communism.

"It goes against the ideals of communism in every way." - HAHAHAHAHA. Ideals are irrelevant. Reality does not care for ideals.

"AI (programmed with basic human values) dictate who would be able to produce the most on what," - I ... I mean... what? If we had an all knowing benevolent AI COMMUNISM WOULD TOTALLY WORK GUYS.

" calculate the amount of work done and allocate resources based on that" - Labor theory of value FOR THE WIN

And for your own education, a private company does not profit off the labor of others. It profits of capital investment, entrepreneurial risk, and producing a profit by offering goods and services on the market. Labor is just a factor and not the most important one.

"waits for society to reach the point of post-scarcity " - lol if only we had post scarcity everything would work.
"In communism no profits are gained" - an economy cannot fucntion without profits. Period.