In general it's more complicated and there are many misconceptions here. About the economic leaps, you can take a look at the USSR, which holds the growth record etc. The country started off in the mud just to end up in space a couple of decades later, while simultaneously fighting off invasions launched by the most industrialized countries of the world. The economic policy was a huge success. The policies of the USSR were different from time to time. In the end you had more opportunists and careerists than socialists at the top. These had an interest in abolishing socialism and in appointing themselves as the new capitalists in the free market Russia. The people of most USSR republics never wanted the union to be abolished, and most people still regard their version of socialism positively. Especially now with the hands on experience with capitalism.
Marx doesn't describe any kind of utopia. The marxist branch of socialism (what is now called socialism) is scientific and opposed to utopian socialism (what is now called anarchism).
Greed is not really a problem. In this society greed and other behaviors are given incentives, they are required for survival. Agents have to act in a certain way to maximize their chances, they have no other choice but to follow the rules of the market. Other types of societies have other incentives and promote different behaviors. None of them are human nature, just as much as slavery or serfdom isn't. They are just ways to organize production as imposed by the level of technology.
Socialism is in fact in the interest of most people. But not all. People aren't socialists because of some altruistic visions, they are socialists because they benefit from a democratic society rather than a capitalist one. And they band up together, in solidarity, just like capitalists band up, to reinforce their interests.
Running a capitalist, free market, society may be completely in line with communist politics, at certain stages of history. Capitalism just like any other system before it has been progressive. For example it would be perfectly valid to support a capitalist system or a liberal revolution as the one in France after 1789. But of course, that was before socialism even existed.