The reason more people aren't richer is because of private property and the capitalist system. As a whole, humanity is pretty rich and is severely destroying the environment to make sure of that. Only a fucked up economic system with all the wrong incentives makes sure some people starve when we produce more food than needed to feed the entire population, sleep on the streets when there's millions of empty/abandoned housing units, etc.
So, to be honest with you, i don't think taxes is the solution, because as long as money and private property are a thing, taxes will only be a band-aid on this cancer. Arguably, taxes are also often misused to fund more human misery in the form of military and police services and other harmful institutions we should entirely get rid of. But i would say claiming high taxes is responsible for poverty is really missing the point of how capitalism works.
Capitalism is only called "least worst" by capitalists themselves. Much of humanity considers capitalism "the worst".
> Give a viable alternative that doesn't descend into fascism
So, to give some historic perspective, capitalism is precisely the root cause of fascism. All totalitarian systems are capitalist by essence, and historic fascism in France, Germany, Italy, Greece (etc) was pushed not by popular support but by industry leaders. Mussolini himself even argued fascism should be called "corporatism" because such was its true nature. If you'd like to learn more about this, i strongly recommend a documentary called "Fascism Inc".
Now, i'm guessing you believe the USSR was a fascist alternative to capitalism. As an anarchist, i understand the USSR to be a form of State capitalism, not communism. Communism is when power and resources are shared, which is what the Soviet (workers councils) revolution was about before the Bolsheviks (Lenin's sect) seized power and murdered the revolutionaries to establish their dictatorship ("of the proletariat", or so they say).
To people in the USSR, the police was the same. The prison was the same. The factory was the same. The same cult of control and productivity plagued their lives under Lenin as it did under the tsar. And the same political persecution hit them with Trotsky's Red Army as with the Tsar's Okrana. If it looks like capitalism, that's because it is capitalism.
So, now that "dictatorship of the proletariat", "fascism" and "capitalism" have been ruled out as potential candidates for making society better, what about an actual democracy (anarchy)? What about a society in which nobody has to worry for a place to sleep and food to feed their children? In which nobody has to work side gigs to pay for education or health bills? In which regulations are decided not by a national parliament full of the worst psychopaths this planet holds, but by a local assembly of peers where people can decide for themselves?
Our current political systems in the west claim to be democracies but those claims fail any form of scrutiny. The designers of our political systems (in France and USA at least) were either slave owners or colonization advocates, and were in any case strongly opposed to women having political rights. For example Jules Ferry, who is revered in France as the founder of public schools, is less famous for his take on how "superior races" had a duty to civilize "inferior races"... which explains how and why the french public school system was used as a tool of colonization to destroy local cultures.
If you really think you live in a democracy, think about it. Were you given any occasion to vote on actual topics? If your neighborhood opposes a national law, are you free to have your own local regulation supersede the national law? Are you free to study how power applies in your country, and to report on it for your peers? At work, are you free to decide with your peers how to manage the company, or is a boss deciding for you? Are you reaping the benefits of your work, or is a boss and some shareholders reaping them for you?
This system is hated by most because it's ruining lives and killing millions of people. Capitalism is just as rude as Mao's rule, you just can't see it if you're part of the tiny privileged elite (as most of us on HN are). If you're looking for alternatives, please read some anarchist/liberation literature. There's centuries of social criticism and ideas on how to improve things... it just so happens the people formulating these are hunted/jailed/assassinated by those in power. A few names to get started: emma goldman, kropotkin, bell hooks, noam chomsky, david graeber, angela davis...
That's very easy to test, by comparing social mobility in countries with more or less progressive tax rates. I think the results say the opposite: progressive tax rates encourage greater mobility (because those taxes go to pay for free higher education, better public transport, mobility initiatives etc)
Perhaps in terms of tax you are right (though I know of at least 10+% differences even between the richer countries, so I doubt it), but the cost of living varies dramatically even within Europe. You don't need to move to a poor/bad part of Europe to profit either, as for example Lissabon is relatively cheap.
Let's say you have some system where your taxed 0% for income < $20k, 10% between $20k and $40k and 30% for $40k+. You currently earn $39k. You have to pay 10% of $19k so $1900, you keep $37.1k after tax. You're offered a $2k raise. Lot of poor people think that you'll suddenly have to pay 30% * $41k so $12k and lose money. But the 30% is only applied to the portion of revenue you get over $40k. With your raise you know have to pay 10% of $20k + 30% of $1k so $2.3k so you keep $38.7k after taxes, so your raise end up being $1.6k. You have not lost anything.
Now the problem comes from social benefits which usually are not regressive and work on a all or nothing system.