If I read you right: I think wealth accumulating around the most successful is a natural phenomenon which is good for as long as the wealthy have and live out fair empathy with respect to the remainder of the population.
A simple UBI issuing paradigm, with a task of nothing more than issuing purchasing power in an evenly distributed manner at a personal level can at best compromise systemic inequality. The degree to which this compromise can have effect should depend of the magnitude of the purchasing power.
A too small UBI will have little effect on the current distribution and relative growth of wealth and power. A too large UBI might induce a counter-pruductive lazy attitude in too many. Giving a little more purchasing power to each individual than for basic essentials will enable entrepreneurial growth, thus beginning to shift the power balance.
One can calculate the cost of survival in terms of units of energy. By then issuing purchasing power by issuing tokens, each with a purchasing power for a unit of energy, one can obtain a currency with a value that is fairly constant relative to the cost of survival. This also implies that the number of tokens issued (say per week) can be constant.
Where purchasing power is applied determines where profit is taken and hence where wealth accumulates. So if the magnitude of UBI can be such that it allows production and trade at a grass roots level it may generate growth of wealth at that level. What one does with the means at one's disposal however remains one's own responsibility.
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It didn't really address the inequality growth problem. Historically, when everyone suddenly has more money to spend, economic rents suddenly increase. It's not hard to imagine how the UBI money would inevitably flow to monopolies (even small monopolies, such as a landlord who rents out a single apartment) so that they're the only ones who ultimately benefit. So, not only would the intended effect of the UBI not happen, but it would accelerate inequality growth.
Inequality will forever be with us, from it's genetic roots up.
Gross inequality grows because the poor are always at the short end of the stick. The only remedy I see for that is to relieve the poor (especially those incapable of self sufficiency or incapable of being productive at all) at least partially of that disadvantage by giving them at least sufficient lasting purchasing power to survive on. Barter economies etc work for the productive sector of the population - what about the rest?
Resolving the problem of sociopathic exploitation of this remedy may require a different strategy...?
I agree that inequality will always exist, but I think that inequality growth has been institutionalised and we need to change that. The system is like a vacuum cleaner, sucking money from the poor and delivering it to those who control the machine. If you give more spending power to the poor, it'll get sucked up, too.
The things is that the vacuum cleaner doesn't belong to the few. It belongs to everyone. Make the people who control it pay rent to the rest of us if they want to use it and pretty soon they may see that it's pointless to use it.
I agree that the problem is systemic and that it is systemic because of human nature. The vacuum cleaner in effect belongs to those who control it - they have taken control of it. Humans are selfish by nature and those in control won't simply hand over control to those without the power to convince them to do so. An independent means needs to be applied to empower the powerless.