I never understood the UBI argument. 30 seconds of napkin math would show you how insane the proposal is, even at the rate of $1000/month. If you want to increase welfare for those below the median income, fine, let's have that discussion. Don't play games with the word 'universal'
The advantage of doing it this way is that it makes it clear what's going on. Right now we nominally impose low marginal tax rates on the poor but their effective marginal tax rates are high because of benefits phase outs, so their effective marginal tax rates are higher than the wealthy. With a UBI you replace the benefits with cash payments and eliminate the phase outs, but also flatten the tax rates so the poor are paying the same effective marginal rates as the rich, instead of higher ones.
The result would be that the poor pay slightly lower effective marginal rates and the rich pay slightly higher ones (although you don't even inherently have to do that; it depends entirely on the tax rate and the amount of the UBI), but the overall system is much simpler. And the consequence that the poor are paying higher effective marginal rates than the rich, which was presumably never intended, goes away.
No one serious is suggesting "everyone gets $1000/month and literally nothing else changes".
The welfare plans that might be subject to being replaced only amount to a few percent of the federal budget. The bulk of the budget is those plans above, which would result in less benefits if replaced. You're not paying for this by finding lost coins in the couch cushions.
Printing money to make the shortfall is how US public sector budgeting has worked for decades.
That said, if we want to talk taxes, I think a progressive tax system is nearly always wrong, immoral, and unfair, so you probably would disagree with any adjustments I'd suggest. :)
The fair way would be if sentences had to pattern match "I think [scheme] is a good idea and we will pay for it by [specific tax proposal].". Seems unlikely in practice though.