You call the American Dream a ‘lottery ticket’ and in some senses it is. Lots of poor people paying into a pot and only a few lucky winners benefiting. Developed countries’ safety nets are more like insurance policies than a lottery. Therefore in such a country, the only logical insurance provider would be something other than a profit-driven company.
Countries that are able to approach equality of opportunity have done so as a result of a wish for fairness and justice. Not only because it’s the right thing to do but also because it’s cheaper in the long run to spend money on education and health care for all. Unlike the U.S. these countries more closely resemble true democracies.
In a lottery mentality, everybody has a disproportionate belief in their chance of winning. The stories of happy winners drown out the daily misery of millions of disappointed losers. That’s why it’s so hard to move away from such a system. Add in corrupt self-serving politicians and you have almost guaranteed that nothing will change until mass discontent forces a revolution.