If you squint at the right angle, this is essentially the argument for "privatizing" Social Security. Even in that limited form it's a huge political loser (for a mix of good and bad reasons, IMO).
Defined rules instead of making up decisions as you go. That is always a tough sell, because it considerably reduces the scope of activity for politicians. Less for them to decide or promise. But that does not mean that we should not try. Imagine the opposite: a state that engages generously in welfare, but only ever in one-time handouts. It would be a perpetual repetition of those in power feeding of all critical mouths.
I think that this is exactly how the Roman Empire dealt with the "automation problem" of their time (a massive increase of forced labor imports -slavery- completely wrecking the domestic labor market). Now where again did fascism's namesake originate? Not really the point, I am convinced that everybody would agree that one-off welfare is a power politicians should not have (even politicians, as long as they are not in power).
No matter where you stand on the question of more or less welfare, I think you should always fight for it being more regulated. Which in the case of welfare, means "de-politicising" it as far as possible.
I am not an expert on central banks and macroeconomics, but I don't see why the Fed couldn't wiggle payroll tax rates around, keeping it revenue neutral by making up any shortfall with the printing presses.
So why not at least tie it to estate taxation? It seems so obvious to me that Varoufakis not mentioning the possibility looks like him being all too careful to avoid stepping on certain feet.
Seize that percentage when they are passed on from someone who (maybe) earned the capital to someone who by definition did not. Convert shares to special "dividends taxed for CCD" shares if you don't want to repeat for each generation and/or you don't want to mess up voting. It would certainly create an imbalance between public corporations and privately held ones, but according to the usual anti-estate-tax arguments that is exactly what you want: don't split up the family farm. But share portfolios are inherently splittable. If the next AT&T or Standard Oil turns out to be a private company due to abuse of this imbalance, forced IPO beyond a certain size might be an emergency hatch option. But that is one of the few problems where i think it is perfectly reasonable to not put too much thought into before they happen.
I do however like the idea of something UBI-like that is not defined by needs (with all their inherent negotiability and the destructive bickering that comes with it) but directly by the capability of the underlying economy.
(edit: removed concrete numbers which i somehow thought were inside the original article, but which i only accidentally picked up from a peer comment)