And there's no immutable law of nature that says a universal basic income would excuse any current or future disputes regarding equality, justice, and fairness. Indeed, UBI could even exacerbate feelings of unfairness in myriad, unpredictable ways.
The fundamental issue is that concepts like equality, justice, and fairness are highly dynamic and often far removed from most objective measurements of well-being.
That's not a critique against those concepts. Our need to feel treated "fairly" is innate. But the reality is extremely messy. The meaning of "fair" is constantly evolving, from the perspective of each individual, each community, and society-wide. And it rarely if ever means the same thing to any two people or groups, and hardly ever means the same thing to the same person across time or other context.
Spoiler: this is where a solid libertarian argument for universal basic income begins. Since we know just about every distribution of property/wealth in the present day traces back to a use of force or fraud in the recorded past, but just about everybody has cause against someone, it would be impossible to equitably settle every case individually in order to create a clean slate on which to build a libertarian society. It would also be impossible to just declare "libertarianism, starting right now" and lock in the current known-inequitable distributions of wealth and property. Adding a universal basic income, given to everyone and funded by taxation of everyone, offers a way around this conundrum.