It's also not clear that it's true in general. Invested money doesn't stand still. You invest it in a startup and the startup spends it. You deposit it in a bank that loans it out and the borrower spends it.
So it could be that taking from the rich and giving to the poor causes inflation or, if startups and mortgage borrowers spend money faster than checkout clerks and bartenders, the other way around.
M1,M2,MZM,M3,and M4 are all affected by fractional reserve banking.
> Under some measures the same "quantity" of money at higher velocity counts as higher money supply (which arguably better reflects the effect on the real economy)
No, velocity is orthogonal to the money supply under all measures. Whether you use a constant velocity model or a variable velocity model, the velocity is a distinct factor altogether, the same way mass and acceleration are different concepts, even though they can be linked by an equation involving the sum of all forces.
In the US, probably. There are some other countries where the amount of money currently being spent on social security is already large enough that it could be reorganized to give basic income to the whole population.
Well - it doesn't, actually.
A self-sufficient program would have to be self-sustaining via tax revenue, and unless the goal is to defeat the whole purpose of the program, the tax revenue will disproportionately come from the wealthy. However, the wealthy are less likely to spend every extra dollar that they have, which means that they're more likely instead to save (invest) it[0]. In other words, this proposal would transfer money that is currently being used for long-term investments[1] and put it towards consumption.
The velocity of money would increase, but the actual supply of money would almost certainly decrease, holding all else equal.
[0] Money stored in the bank is an investment; it is the source of capital for others who want to procure loans for investment and infrastructure projects.
[1] These deposits create money, thanks to fractional reserve banking