Your logic is based upon the premise that a more socialistic society is a more stable society, yet that is hardly what we see in reality.
North Korea is incontravertably more socialistic than is the U.S., yet to maintain "stability" in North Korea requires the massive daily intervention of the police state.
Cuba's "stability" is so fragile that it FORBIDS competition to any elected office. Sure, the people can vote, but they only get to vote for the officially annointed candidate. And Cuba is clearly more Socialistic than is the U.S. or even Canada.
The Soviet Socialistic Union [Soyuz] Republic, known in Cyryllic as the CCCP and in English as the USSR, was likewise more socialistic than was the U.S., and was demonstrably less stable.
In sum, your premise appears to be flawed based upon the known examples of socialism that are available to us.
In fact, one could make a very strong case that the more a society tends towards socialism, the less stable it becomes.
Sure, a social "safety net" initially makes good sense, until said safety net becomes abused to the point where the participants are better off remaining in the safety net than if they returned to the work force (when/if able). Moreover, that direct-cash-payment safety net may make less sense than a community "poor farm" or "poor house" (or not, collectivism seems to fail everywhere it is tried).
Worse, the net effect of any large-scale transfer of wealth from the rich to the poor invariably manages to remove investment capital from the most productive members of society - in favor of transferring said capital to the least productive members of society, a recipe that by definition means "lower productivity" for society at large.
And when society at large has lower productivity, it means that all boats are sinking, not rising (a trend that invariably leads away from prosperity).
That is socialism. It sounds good initially. It feels good while its happening. It might even look good at first, and then history kicks in to reveal that socialism leads to declining productivity/wealth.
Cubans drive the SAME cars today that they stole from Americans in the 1950's, for instance. North Koreans don't even drive. That's not 21st Century wealth, that's medieval poverty.
And that is the endgame of socialism. In the end, it redistributes not wealth, but poverty (and everyone "feels good" on the ride down).