Ironically, I suspect a UBI not only can coexist with inequality but might substantially increase it (not a bad thing in my book). The vast majority of Americans already have incomes above a UBI level, especially when current government benefits are accounted for. But post UBI, a substantial minority would exit entirely from market labor, while another substantial minority would be more willing to take career and entrepreneurial risks that are on average income increasing. There are also some very favorable aspects of it for marginal tax rates, which would encourage workers to earn more income.