You know why unions even exist? Because there is an inherent difference in bargaining power. And that is even with bargaining.
Even if I accept your argument as true, the simple solution is to allow unions.
And I don't accept your argument as true. When I was a first year lawyer, yes, I had little bargaining power. By the time I was a fifth year lawyer I was billing $1m a year for my firm and I was gently, nicely holding it to ransom till I got what I wanted...and even then they wouldn't pay me enough so I took my long-service leave and left. I could have done anything I wanted - I held all the chips.
Anyone who's good enough gets the bargaining power. Someone who's not good enough gets the safety net of universal basic services and unions.
Why not just the money instead and safe all that inefficiency inherent to vouchers?
As I stated before, I have absolutely no issue with giving someone $20k in cash a year instead of $20k in vouchers; the problem is, though, we'd have to agree that if they misspend the $20k or use it on shit (drugs, gambling) instead of what it's meant to be used for, there's no more in reserve. Otherwise we're paying people multiple instalments of UBI.
So that's the issue really - UBI is never enough, if given solely in cash form, unless you're going to tell me that someone who spends it immediately on drugs is then going to be turned away from the food bank?
And UBI by itself, even if it was enough to theoretically counteract all the inequities in opportunity that we genuinely want to counteract, won't do so unless everyone spends it rationally - which they won't.
So if we used your idea and gave everyone cash instead of vouchers, and people didn't spend it rationally, I bet you'd be saying we didn't have enough redistribution. Even if we did.