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?
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).
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.
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.
(... amusing to consider, probably not participate in.)