Having a smooth bell-like wealth distribution is healthy. Communes don't work for large communities. Communes do work and can work well in small doses (e.g. Kibbutz today and utopian/communistic communities in 19th century America). Experimental results show collective communities starts to break down when population size is in the thousands. We know the lower bound around 4 people work out very well in human history. We call that a 'family'.
When wealth distribution becomes skews or have double spikes, there will be social chaos or even revolutions. In small city states it is possible to have a very large wealthy population and smaller relatively poor population. The threshold seems to be around 15 million. For larger countries, it is far more likely to have a much larger poor population with a rich minority. When the poor feel the current system is unjust and they have nothing to lose, they will rise up (especially the urban poor since they have more spare time and education). This is why having a dominant middle class is the best way to ensure social stability. Today, the U.S. income distribution has been diverging since the Reagan era while China's middle class is growing mainly through urbanization.
The key to longevity for any political system is to provide a mechanism for social mobility so the ambitious poor know they have a chance for successful if they choose to. Chinese have an old saying that wealth does not extend more than three generations. That is social mobility (poor gets rich, rich gets poor). A good system allows a political system to last for millenniums like China's examination system still practiced by every East Asian country today (the dreaded college entrance exam). Bad ones can lead to wars and conquests like 19th century Prussia and Japan where rising up socially through the military system is encouraged and promoted.
In the end, a country's political system is not nearly as important as its economic system. The two are independent but politicians (in the U.S., China, and everywhere else) like to brainwash you into think they are one the same (convincing you to swear allegiance to Apples by showing you how sweet Sunkist Oranges are). In the economic sphere, what most people seek is fairness/equal opportunities (for those that wishes to compete but keep in mind that there is a large population where material wealth is not their life objectives). If the level of fairness is good enough, the political system is viable.
In game theory, there is a simple 'fairness' test. You can ask yourself what would you do if you are A and if you are B. I won't post the answer (minimum amount for over 50% success) here. You can easily google it. The answer explains what astute politicians already know.
Two people A and B on how to share $1. A decides how to divide up the dollar. B decides to accept A's deal or not. If B accepts, both get A's allocations. If B rejects, neither gets anything. For example, if A decided to give himself 1c and leave 99c to B, chances are B will accept. Chances are if B is only offered 1c and A wants to keep 99c for himself, B will walk away. If you are A, what would you do? If you are B, what is the minimum amount you'll accept?