I don't think Uncle Karl was proposing a 'flat organization of society"; he wasn't a radical an-archist, after all, bent on eliminating every trace of hierarchy. You seem to be supposing that the ideal socialist arrangement would be 'flat' -- no hierarchies sticking up above the plain of equality.
Some of the problems impinging on equality among workers are the province of human psychology and group dynamics. These human factors--ambition, cliques, group solidarity, insiders/outsiders, individual manipulations of the group and other individuals--will abide for ages to come, with or without a workers paradise. So, a primary task of people living in this workers paradise will be to self-manage the features of human psychology that work against social harmony.
Remember that phrase, "from each according to his abilities, to each according to his needs". Everyone will have the exactly the same level of responsibilities, nor will everyone receive the same rewards. Some workers (say a worker with 5 children) will need more pay than a young single. Similarly, some workers will present managerial talents rather than excellent eye/hand coordination. Managing involves more complicated tasks than parts assembly. That doesn't mean that the manager deserves to be living in a penthouse. Managing the flow of work is just another job at which some people are better than others. A much higher level of thinking will be expected of brain researchers than will be expected of enterprise managers. Brain research is a job. Just because it is highly specialized and technically demanding, doesn't mean the brain researchers should live in palaces overlooking the ocean.
This idea isn't altogether unknown and untried. The abbot of a Benedictine monastery has power and responsibilities greater than the average monk, but he still lives in a room like the other monks live in and eats the same food.
Marx didn't lay out a blue print for a socialist society. The first seizure of power, where the capitalist possessors are dispossessed isn't the heart of the revolution. A redistribution of land isn't the critical step either. There are several preliminary steps. The real revolution is when the workers (who are, again, almost everyone in a society) begin to devise the kind of socialist economy and way of life that is workable and acceptable.
A revolution can't be sprung on people. It's absurd to think that way. The Bolshevik Revolution in Russia, leading eventually to the formation of the USSR, happened TO the people. The Maoist revolution in China happened TO the people. So, HOW a revolution comes about is a critical thing. I prefer a revolution that is the outcome of extensive organizing, political work, and education. If the final step has to be violent, so be it, but in many cases the violent element can be minimized.
The people have to be involved in thinking about what kind of society they want, really, before the revolution begins. Hence, organizing, political work, and education. The instantiated revolution has to come FROM the people, not happen TO the people.