I agree, that's why I support a system that benefits them the most, free market Capitalism and a government that does only what it should.
Wouldn't the market be freer if we slowly replaced that minimum wage with UBI (i.e. decrease minimum wage and increase UBI over time). The market would then be free to set prices more accurately because there would be a lower artificial price floor. This also helps create more jobs to offset the ones lost to automation, since people can afford to be paid less, a wider variety of jobs can be economically viable. Additionally, people would have more freedom in find jobs that they enjoy and are well suited for. All of this would increase economic efficiency.
Thus, yes, UBI could benefit everyone by making our labour market freer and more efficient. Basically, UBI is a form of economic infrastructure, and thus is a MORAL thing to spend taxes on.
That is an assertion/opinion, not a fact. You are also confusing a problem (poverty) with a solution (minimum wage). There are many other ways to tackle poverty that don't involve distorting labor markets with minimum wage. There is also a strong argument to be made that a minimum wage that is above market prices hurts low-skilled workers by making it illegal for them to be employed.
Personally I'd rather have the challenge of supporting people with low-paying jobs vs the challenge of supporting people with no job at all.
If that were true then we would switch to a better system. I don't think it is and I don't think there is one.
I don't know what capitalism's logical extreme is but if you are talking about anarchy then I am not for that. I believe government serves a very important role in capitalism. It enforces contracts (legal system), protects third parties (environmental hazards), and defends against foreign or domestic aggression (police, military).
This isn't to say capitalism is perfect! Of course not but it is better than every other conceived system and has proven so by bringing millions out of poverty.