I'm explicitly talking about how to make the UBI work without the massive income disparity, not lower work hours as a seperate solution. Should have made that more clear.
The lowering of work hours for those still working has the effect that more people still work, with UBI to lower the impact on their income loss. This way the tax revenue can remain higher because more people are still providing a net contribution. This is necessary because, well, the UBI has to be paid somehow. Of course, with lower work hours the taxation for lower incomes has to be increased, or at least it has to be made sure that the total tax revenue is still high enough. To make clear what I mean:
10 people earn 10k per month for fulltime job, pay 50% taxes for that, so 50k tax revenue for ten people working full time. Consider a UBI of 1k, and twenty people working half time. Twenty people, earning 5k per month, still earning the same 100k before taxes. But would they all pay the 50% tax rate still? If so, they'd each earn 2.5k per month (3.5k after receiving the UBI), 50k in total (70k after UBI), and 50k tax revenue. That's great, but what if 5k per month puts them in a lower tax bracket? Let's say, 25%? So each pays 1.25k in taxes, leaving 20k in total tax revenue for those twenty working people, and each with 3.75k per month earnings. Plus a 1k UBI, so 4.75k for each in total.
Just to make it clear that the taxation has to be taken care of. Let's say you have a certain population that you need to take care of with the UBI, so with the 50k tax revenue from the ten full time or 20 half time workers at the same tax rate you could provide UBI for 50 people in total. If the 20 people pay less taxes, though, the tax revenue suddenly drops to 20k, so only 20 people can receive UBI from that.
So the tax rate has to make sure that the budget is fullfilled. And to get the tax revenue at whatever tax rate, people need to get paid accordingly, that's the whole point.
However it's done, the budget has to be taken care of. It can be done, especially in a country like Germany with an already very high tax rate and lots of social programs that coul dbe replaced.
But it has to be done carefully, without lying and pretending that half a trillion more than the entire budget is a totally reasonable cost.