I disagree with your premise that doubling the number of dollars everyone has would simply double prices. If you take someone that has $1 million in the bank, and magically make that $2 million, they almost certainly won't double all of their expenditures (they probably wouldn't change what they spend at all on a wide variety of categories - food or clothing, for instance). Rising inequality means that lack of demand is actually a big issue, since we're transferring income from people that would readily increase consumption, given more income, to people that will largely sit on that money. Globally speaking, our factories could easily produce more goods without raising prices much, if any. I believe a UBI would effectively be a transfer of wealth from people that have lots of money (but don't spend it) to people that don't have lots of money (but would readily spend more if they had it), but it wouldn't be the zero-sum game that people often assume it would, just by virtue of our productive capacity not being nearly maxed out.
While the now $2 millionaire would not be likely to spend that extra million on food and clothing they would be extremely likely to invest that money in a variety of financial instruments, making that capital available in the market so it can be put to good use. Investing does help inject value into the economy and drive growth - "sitting on it" would require literally keeping it in cash in a bank, which no sane person would do due to inflation.
> they would be extremely likely to invest that money in a variety of financial instruments, making that capital available in the market so it can be put to good use
This improves the supply-side of the economy, but doesn't do anything to stimulate demand for products. Today, lack of demand is a larger problem than increased output. The labor share of GDP has been decreasing since the 70s, and its starting to hit levels where people are having trouble affording as many goods. Although investing is a good use of funds, arguably redistribution (a type of demand-side stimulus) would be more helpful today.
Juicero and their ilk prove that there's too much capital looking for somewhere to go. We don't need this much capital floating around, we need peoples' lives to improve so they stop killing themselves with heroin.
"sitting on it" would require literally keeping it in cash in your safe. If put "in a bank", unless you mean a safety deposit box, is (to some approximation, in theory, in the not to distant past, maybe) reinvested by the bank. That is how the bank makes money.
