This isn't entirely accurate. What you described is a 'socialist' community, the so-called 'lower stage of communism'. In this stage, there would still remain incentive based structures for labour. It employs a policy of "from each according to his ability to each according to his works". Inequality still exists as explained by Marx here:

This equal right is still constantly stigmatized by a bourgeois limitation… one worker is married, another is not; one has more children than another… Thus, with an equal performance of labor, and hence an equal share in the social consumption fund, one will in fact receive more than another. — Critique of the Gotha Programme

It is during this lower stage that the transformation of social relations and productive forces gradually alters the motivations for labor to a more virtue-based one.

The problem most communism skeptic people have with communism is that they reason within the current modes of subsistence and assume it is impossible.

“What we have to deal with here is a communist society, not as it has developed on its own foundations, but, on the contrary, just as it emerges from capitalist society; which is thus in every respect, economically, morally, and intellectually, still stamped with the birthmarks of the old society from whose womb it emerges.” — Critique of the Gotha Programme

Marx also stated that he expected us to remain in the lower stage of communism for centuries, but it is during this stage that we prepare the productive forces to sustain communism and start producing goods for their use-value rather than for their exchange value, so that we can achieve the higher stage of communism which employs 'from each according to their ability to each according to his needs. This higher stage is truly classless because we would supposedly have solved scarcity, it would be stateless because people would organize communally to meet their needs, and it would be moneyless because the means of production and means of subsistence would be free for all to access.

In a higher phase of communist society, after the enslaving subordination of the individual to the division of labor… has vanished; after labor has become not only a means of life but life’s prime want… only then can the narrow horizon of bourgeois right be fully left behind and society inscribe on its banners: ‘From each according to his ability, to each according to his needs!’ — Critique of the Gotha Programme