Response to government helps against income inequality

Response to: https://twitter.com/AtheistBigfoot/status/735497377109266432
Context, a discussion about the results of government:
CriticalThinker (paraphrased): "Government control, even with the help of economy professors, is nothing compared to letting millions decide with their wallet"
BigFoot Monday: "If 1,000,000 people have less money than 10 people, guess which wallets speaks loudest?"

There's so much wrong with this, I'm putting it in a paste bin instead of in many tweets.
Government increases income disparity between people, not freedom. Remember, it's about results, good intentions are a start but not good enough.
1. Welfare keeps the poor in poverty: https://fee.org/media/4182/0712lingle.pdf
2. Inflation destroys the value of people's savings and income: https://fee.org/media/4484/hazlitt1104e.pdf
  Governments create inflation on purpose so paying back the money they loan, is less of a problem
3. Government education harms the poor because it's shit and the less educated will just accept it. Where the well educated will understand government is doing a poor job and demand better education, so the quality of education becomes related to the education of the parents, further increasing the social divide
4. Socialism harms the economy, meaning that everyone will be worse off
5. To avoid these negative effects the rich buy off the government, so they are compensated and protected from competition/failure
6. Protection includes protection from competition, which harms the poor the most

All together this situation of the few having much and the many having little is created by government. In a free market the rich will really have to compete. If they try to create a monopoly, they will be ignored, socially shamed and/or out competed by others who are not spending money on creating a monopoly. This means companies will fail more often than now. Which is a good thing, bad companies are wasting resources, those people are better off doing something more valuable, even if it hurts in the short term. Income inequality was much less with less government and is much less now in countries where government has less power.

Government also forces the very difficult problem of having to agree on rules that will apply to everyone. This is difficult since everyone is different and therefore wants different stuff/rules and reaches different conclusions, even with the same information. That creates a lot of division in the community because other people wanting something you don't want, affects you.

With the free market this is much less of a problem. A much smaller number of people wanting something is enough to make it happen, to allow a business to profit from it. And if there's not enough in your community you can go elsewhere get it there, come back. There is no need to force rules on people they don't want. There can be value in creating consistent rules that everybody follows, in those cases people can work together to create those rules just fine. Competing companies do this all the time, sometimes it takes many years. The difference with governments is that when people don't like it or it doesn't fit them, they can always choose a different solution. Someone else having a bigger pocket is not an issue for you, they get what they want and pay for it, it doesn't harm you.