Ambition is what drives humanity forward, for better or worse. Unless you can channel the needs of the state as a replacement for personal ambition, your society under communism is unsustainable. This is very difficult to do without reverting to a society that is either 1) capitalist or 2) utterly corrupt.
Either way, communism is self defeating, and therefore dangerous.
EDIT: Just to note that I upvoted you and encourage others to do the same. This is a place to share knowledge and you asked a perfectly valid question that many people have. This is not reddit and nobody should be downvoted for asking a question, regardless of how basic it might be.
It really doesn't matter if they are or not. In order for communism to truly work, you'd need to abolish all rewards. That is, the very act of having hockey players and cosmonauts and musical talent recognized by the state at large - regardless of financial reward - creates the very imbalance that communism is supposed to address. As I said: self defeating.
People may seek different rewards based on their character, but the very nature of man is that we work best when challenged and respond will to the rewards earned when overcoming those challenges, financial or not.
If your economic system essentially requires a man with a gun to ensure and enforce its existence, there is something wrong.
To put it simply - when all the wealth is equally spread, there is no incentive for anyone to do anything. If everyone is paid equally and has the same benefits, there's no point in working harder or smarter - you just do the bare minimum and be done with it.
Let's take a capitalist factory: workers are paid $5 per assembled iPad. Those who want more money can assemble 100 iPads and make $500 in a day's work. Most are happy with $100 per day, so they'll assemble only 20 iPads (let's say that's the minimum amount required).
Now a communist, state-operated factory: workers are paid $100 per day because everyone is equal. Those who want to make $500... can't, even if they assemble 1000 iPads. So they just assemble the bare minimum of 20 and are done with it, secretly cursing the government for this injustice/inequality (how ironic is that?).
The overall production level drops significantly unless the state raises the minimum amount of iPads made to 100 per day. Obviously, the people who are happy with $100 per day are now pissed off, either because they don't want or simply can't work that hard.
The only ones benefiting from communism are those who make the laws and control the factories/country.
I don't think this is true in general, though it's true for some jobs (mostly jobs that nobody wants to do). For example, I don't think scientists, or even most HN types, are motivated solely by money, and would just sit around drinking beer if they couldn't make more money. Many of us are more motivated by science and technology. Making money is nice, but I would still work on tech if it made absolutely no difference to my salary. The reward is finding interesting things, gaining recognition for my ideas from my peers, etc., not just some monetary bonuses.
If anything I think there's a slight negative correlation between in-it-for-the-money and quality in science. The people who are there to optimize money are usually good game-players, adept at working the system and working their way up bureaucracy. Brilliant scientists often aren't even very good at that, and are more often really driven by the science first, perhaps peer recognition second, and maximizing money a distant third.
I think you are confusing a "planned economy" with "communism." But even then, there is nothing in the definition of a planned economy to say that all people in a certain position have the same daily wage. The Soviet union had an incentive system. For example, http://www.tandfonline.com/doi/abs/10.1080/09668134908409742 says "encourages the foremost collective farmers by means of adding extra labour-days."
You idealize the idea of the piece-rate system, without realizing that that's the system used in the Soviet Union during the Stalinist era. Read in http://en.wikipedia.org/wiki/Wage_reform_in_the_Soviet_Union... how the Khrushchev era reform movement pushed to move from a quota system to "standardising their wages and reducing their dependence on overtime or bonus payments."
From that page, "The piece-rate system led to an enormous level of bureaucracy and contributed to huge inefficiencies in Soviet industry. In addition, factory managers frequently manipulated the personal production quotas given to workers to prevent workers' wages from falling too low."
So it seem that your "capitalist factory" is using the same piece-system incentive system as used during the Soviet era, which is about as communist as you can get.
I also think you are confusing "capitalist" with "meritocracy." The US during the period of slavery was under laissez-faire capitalism, but quite obviously slaves did not enjoy the same benefits which you attribute to capitalism, and a slave working the same job, with the same abilities as a free man was unlikely to make the same rates.
You write "Obviously, the people who are happy with $100 per day are now pissed off, either because they don't want or simply can't work that hard." Or they might put their family life ahead of the company's bottom line and think that 40 hours of week is enough even if some people want to work 80 hour weeks.
Finally, you wrote "The only ones benefiting from communism are those who make the laws and control the factories/country." There's nothing unique to communism there. The same holds with capitalism. If only the richest 1% in a capitalist country make the laws and control the factories/country, then it's very likely that they are benefiting the most. The economic system and the form of government are not as strongly coupled as you suggest.
There you go, I think I fixed communism.
http://en.wikipedia.org/wiki/History_of_communism http://en.wikipedia.org/wiki/Great_Purge
If you'd prefer text here's one: https://thesnarkwhohuntsback.wordpress.com/favorite-passages...