You continue to misunderstand the communist position. You are projecting liberal idealism onto a framework based on historical materialism. You still seem to think we expect the state to be abolished by decree or that its existence relies on the graciousness of future leaders. This is entirely backward. The state is not a moral entity held together by the goodwill or greed of individuals. It is an instrument of class suppression dictated by economic relations.
Once class division becomes a thing of the past, which is structurally inevitable following the comprehensive collectivization of the means of production, the state simply ceases to have a material purpose. When an institution loses its underlying economic justification, it does not need to be ceremoniously abolished. It withers away as obsolete waste. If a prison has no one in it, it is only a matter of time before it is repurposed for something useful to the community. You do not need a committee of wardens to vote on dismantling an empty prison. The guard force naturally dissolves because maintaining it defies basic logic.
You ask what mechanism decides when the time is sufficient. The mechanism is the material development of the productive forces and the conscious reorganization of the relations of production. Under the dictatorship of the proletariat, state power is held collectively by the working class to suppress the former ruling class and organize socialist construction. As class antagonisms disappear, the coercive apparatus of the state naturally recedes into mere public administration. The government of persons is replaced by the administration of things and the direction of technical processes.
Also, you fundamentally conflate two distinct theoretical concepts. Marx's theory of alienation and his definition of capital are not the same thing. Capital is a very specific social relation characterized by the extraction of surplus value from wage labor to generate profit. When the means of production are collectively owned and production is planned for social need rather than market accumulation, capital simply ceases to exist. Alienation is the broader estrangement of humans from the products of their labor, the act of production, and their own human potential.