Would basic income make the society really more equal? I find it quite difficult to estimate how would it turn out in practice. Wouldn't a more nuanced system give better results?
First, it's a form of redistribution of wealth: assuming it's used with a progressive system of taxation.
I completely agree that we can't know how it will turn out in the long term (but why not try it and scrape it if it doesn't?), but the idea is that individuals could use the income to retrain when forced out of work, and to be able to provide an environment for their kids that give their them at least a chance at upwards mobility.
Again, I don't think it will lead to perfect equality. Nor is it a magic bullet: one pet-peeve is that everyone seems to be concerned with income, but less so with wealth per-se. Some people have proposed a tax on land itself but not improvements to land: I am not trained in economics so I can't speak to its efficacy (perhaps it's an outmoded idea today), but from a moral standpoint such a tax (with perhaps a "homestead exemption" for one's primary residence up to a certain value) seems a lot more fair than an income or property tax (which also taxes improvements to property that benefit the community).
The main problem I see is that basic income would require a much richer society. If you want to have a system that gives a livable income to all unemployed people PLUS gives a significant income bump if someone gets employed, you need lots of money.
Today, everyone consumes the necessary amount to survive. If they didn't, they'd be, well, dead. I guess the relevant point is that few people, at least in Western countries, are dying of starvation or exposure (and those who do usually have severe mental illness).
This means that even with the particular kinds of capital arranged in the particular way we do today, we can produce enough goods so that everyone consumes enough to survive. It's just a question of financing. Most people at the lower end end up financing the consumption either through personal debt or through imposing negative externalities on society, be it theft, drawing down the resources of friends or family, or soaking up charity dollars that could be more effectively used as capital investment. And personal debt just kicks the externalities toward the future, with the additional option of bankruptcy, which increases lending costs for all borrowers, itself a costly externality.
A basic income makes these externalities legible and puts the finances on the books instead of off of them. In addition it gives psychological security and improves the negotiating power of everyone.
The points you raise are good ones, but the question raised wasn't the cost of covering those at the bottom, it's the cost of also distributing it to the rest. Of course, if you couple basic income with an additional flat tax (that is, add X% to all tax brackets) that covers it, you would - net - be giving a lot of improvement to those at the bottom, asking a lot of money from those at the top, helping those just below the mean a little, and asking just a little more from those just above the mean. Of course, there's all the usual concerns around changes in tax rates (including tax evasion) still apply...
Of course but if you compare a basic income system with a more complex and nuanced system (ala developed world today) – and set both to the same level of redistribution – would the basic income lead to a more equal society?
It removes sharp cliffs as benefits are removed, which encourages work. It provides people the freedom to actually meet their most pressing needs (and allows competition to meet those needs cheaply and effectively) rather than the set of needs we guess will be most pressing. Those who, per their situation and opportunities and values, have better things to do will be more able to work less, which might make room for those who more need the opportunity - examples might be one spouse staying home to watch children and keep house, or someone pursuing their art or music, or volunteering at any of the remaining important causes.
All that is aside from the basic dynamic of "taking more money from those above the mean and giving more money to those below it" inherently pushing a bit toward more equality.
