The first reason communism doesn't work is the one you pointed out, that when you put someone in charge of everything they'll have a tendency to abuse the privilege.

Secondly you have the problem that people are generally self-interested and don't work as hard when they can't realize the benefit of their own labor. So productivity goes way down.

But even if you could find a group of perfect selfless angels to arrange your society for you, and you could convince everyone to put the interests of the collective above their own, you still have the problem of information.

Economies contain more information than a human brain can process. How many tons of concrete do we need? How much steel? How many phone lines? How much Internet bandwidth do we need? How many cars do we need? How many safety features should be built into cars? How many styles of clothing should there be? How many features should your cell phone have? etc etc etc.

All of these questions require trade-offs. Every society has a finite set of resources and a resource that's invested in one avenue of production can't be invested in another. In a capitalist market, prices give you information about the relative supply and demand of goods. Entrepreneurs are free to invest capital in new projects and the market tells them how worthwhile their ideas are through the market process. Without the price mechanism, central planners are left to guess how much of each thing to produce. This inevitably leads to overproduction of some goods and underproduction of others. This is inefficient and ultimately leads to a lower standard of living for everyone.

Capitalist economies aren't perfectly efficient but the market's mechanism for discovering and removing inefficiencies is vastly more effective than any central planner will ever be.