These are good questions; I'll try to give you good answers.
// If it’s funded by a flat tax, then yes, but then what’s the point? Seems like nothing more than a shell game. //
yes.
// If it’s funded by a progressive tax, then how is it anything more than a tax increase combined with increased welfare? //
A couple of points:
1. We actually already have UBI and a single-payer health care system--you just have to be 63+ to get it :-) Social Security is the very paradigm of (as you put it), "A tax increase combined with increased welfare." And yet, everybody seems to love having it, or not having to pay for their parent's and grandparent's housing and medical bills.
2. If we had a UBI--say one that paid proportionally to our GDP--nobody would be fearing AI, robots doing the dirty work, etc etc. Every voter would be massively incentivized to vote for public policy which would have our GDP growing as fast as technological progress could let it. This alone, IMHO, is worth the price of admission.
3. I'm going to go out on a limb and guess that you are a big fan of Hayak? :-) UBI is a cornerstone of Hayak's "road outta serfdom." Imagine driving an Amazon truck--and being told when you can and when you can't go to the bathroom. You probably don't have to imagine your employer putting key-and-mouse monitoring systems on your computer. If somebody can tell you not to go to the bathroom when you need to, and if somebody can punish you for not pounding your keyboard fast enough, lets face it, you don't have any freedom. UBI would give us the leverage we need to exercise our inalienable right to freedom even at our workplaces.
// Either way, seems like nothing but a recipe for inefficiency and increased government bureaucracy. //
As others have noted, it is quite the opposite. Think about how MANY different ways the government subsidizes things...sugar prices, corn prices, beef prices are all artificially high because farmers get subsidies. And we're just getting started--oil companies getting subsidies, subsidized student loans---and there are *square miles* of buildings staffed with people to administer them all.
Literally (not metaphorically, or hyperbolicly) literally *square miles* of bureaucracy would no longer be needed.
And if we had UBU--it would be OK to lay them off!