The major problem with communism is that it doesn't take into account the true nature of people and therefore sounds much better in theory than it works in the real world.
Wealth distributed equally
Who distributes the wealth?
The leader/dictator/government
Do you trust the people running things to actually do this?
Let's say we get lucky and the first leader of this communist nation does his job well, and distributes the wealth equally, treating himself exactly the same as every other person. What happens when it's time to get a new leader? How do you pick a trustworthy successor, and how do you keep them honest? Frankly I find it impossible to trust people to not pinch a little off the top for themselves, their friends, etc. This would be a problem that would keep getting worse over time, to the point that the people at the top live a more or less secret life of luxury and opulence with everyone else living in poverty. Equal poverty.
Property is owned by the state
This is the part that sucks for all the worker bees. How hard would you work if you got the exact same distribution of wealth (i.e. paycheck) no matter what you did, and you couldn't be fired? Economics teaches us that
people respond to incentives, and communism gives no incentives for hard work, critical thinking, innovation, progress, etc. The only incentive anyone would have for doing anything is patriotism. That's it.
If you have a small community, patriotism could be enough, because the people performing would actually see the fruits of their labor.
Also, not all of your facts are correct. Democracy, totalitarianism, education and health care providers and freedom of the press are all things that have nothing to do with a country's economical system.
Freedom of the press is just a thing America's founders wanted to have prominence in the Constitution, in response to England's lack of it at the time.
Education and health care can be public or private. It boils down to if you want to pay the schools and hospitals more directly, or if you want to pay them through taxes.
Democracy and totalitarianism along with republics (America is more of a republic than a democracy. More precisely, America is a democratic republic), monarchies and others are just systems of deciding who is in charge. A totalitarian communism doesn't even make sense, because by definition the ruler is not equal. A democratic communism actually makes a lot of sense, and that sounds like a nice place to live. Everyone gets an equal say in every decision and an equal share of the wealth. In America, we call these places hippie communes. Read up on them, if you like:
http://en.wikipedia.org/wiki/Commune
Edited 2/14/2015 01:25:42