Your opening point about advantage reminded me of a story I read years ago. It was in some dense Russian tome - I want to say Brothers Karamazov, but I don't know and don't remember. Anyway, it's not mine.
Once there was a farming village in a valley, Their lives were generally peaceful, except for every few years, a band of ruthless bandits would ride down out of the mountains, sweep through the village, kill a bunch of men, rape a bunch of women, steal everything they could, and ride back into the mountains.
Then the village would rebuild, and after some hardship, replenish their crops and livestock and supplies... then the horsemen would ride back down, kill, rape and steal, then ride away.
This went on for many years, until the time that a different band of horsemen rode down from a different part of the mountains, and they killed, raped and stole, then rode away.
Then, shortly thereafter, the customary band of horsemen rode down, only to find the village devastated and everything they intended to steal already gone.
When they found out what had happened, they realized that that could not be allowed. They lived lives of ease through killing and raping and stealing, and they weren't going to give that up, but they couldn't do it if things continued that way.
So they struck a deal with the villagers. The villagers would provide them with everything they would've stolen if they could've, and in exchange, they'd not only stop killing and raping them, but make sure these other horsemen didn't kill or rape or steal from them either.
And the villagers, wanting only to live their lives as unmolested as possible, reluctantly agreed.
And thus was government born.
Technically, no - there has never been a truly communist society. They've all really been communist in name only.
In order for the society to be truly communist, property must be communal - that's the fundamental requirement.
And in order for property to be truly communal, all must have an exactly equal right to it, or more precisely, an exactly equal right to share in control of it.
The moment that hierarchical authority is introduced, control over the society and its property is tied to that authority. The right to exercise control over property is vested not in the people communally, but in the system by which authority is designated and exercised - the state. And that means that for all intents and purposes, regardless of any claims to the contrary, all property is actually owned not by the people, but by the state. And that is not and cannot be communism.