The problem of too low UBI seems the biggest practical one. And if we do it somehow needs-based, then it stop being universal, which is one of the supposed advantages - that it absolutely eliminates administrative costs/problems/etc. (But of course those are very fine straw men. Rationally none of those matter. Only that we somehow synthesize a long term (eg. sustainable) strategy to solve the problems that every kind of income/wealth redistribution aims to solve.)

Of course with that attitude we're quickly back to where we are now, needs based assistance programs. Plus a lot of recommendations on how to change them. One of them is that we should stop fucking around - to use the expert terminus technicus - and just give poor people money. Yes, they might even spend it on things that give them some pleasure on the very short term. They might even buy drugs. Not that they can't do that now with some extra steps. (Buy a-okay food with assistance program, sell it for cheaper, buy booze.)

And you are exactly right, the inequality is again completely independent of UBI. It depends on taxes, labor's share of income, etc.

UBI is a magical unicorn, it is assumed to provide everything good. Especially because it's so vague most of the time. (That's why talking about NIT is much easier, it's a rather concrete form of UBI.)