Authoritarian communism, is , from my perspective, not genuine communism.
Isn’t a core principle of communism (as the term itself implies) a communal society.
"Communism" is a moneyless, classless, stateless society. But while communists see this as an end goal, many don't believe it's possible to go directly to that. Colloquially, the term "communism" is sometimes used to describe a society in which communists hold power, even if it has not reached that ideal, i.e. "Communist China," although the more acurate term for that is "Actually Existing Socialism" or AES.
Frederick Engles argues for the necessity of authority in "On Authority:"
All Socialists are agreed that the political state, and with it political authority, will disappear as a result of the coming social revolution, that is, that public functions will lose their political character and will be transformed into the simple administrative functions of watching over the true interests of society. But the anti-authoritarians demand that the political state be abolished at one stroke, even before the social conditions that gave birth to it have been destroyed. They demand that the first act of the social revolution shall be the abolition of authority. Have these gentlemen ever seen a revolution? A revolution is certainly the most authoritarian thing there is; it is the act whereby one part of the population imposes its will upon the other part by means of rifles, bayonets and cannon — authoritarian means, if such there be at all; and if the victorious party does not want to have fought in vain, it must maintain this rule by means of the terror which its arms inspire in the reactionists. Would the Paris Commune have lasted a single day if it had not made use of this authority of the armed people against the bourgeois? Should we not, on the contrary, reproach it for not having used it freely enough?
If we're at the point of saying that Marx and Engles weren't "genuine" communists, maybe it would be better to just chose another word for what you're describing, because most self-described communists around the world are Marxist-Leninists, or "tankies."
No single leader would be needed. And would always cause a failure of the system.
A rotation of elected counselors would be optimal.
Both the US and China (as examples) already have "a rotation of elected counselors," do they not? Both have a congress of elected representatives which represent the highest legal authority. Or do the president/general secretary count as "a single leader?"