The newly printed money is credit to the private institutions, who must repay the printed money with interest. You're not getting a system less skewed towards the rich by replacing that liability with one towards high net worth individuals or hedge funds instead...
Saving makes sense in a deflationary environment, its just that "saving" involves letting other people do productive things with the money with rather than starving them of funds in the hope they will be sufficiently desperate for cash in future to be willing to exchange more stuff for it. A deflationary environment sets a floor on how much the 1% control, not a ceiling, disincentivises them from creating jobs (lots of risk, no aggregate money returns to be earned) and makes it risk free for them to starve the economy of resources instead.
And in a world with no "crippling mortgages", you still need somewhere to live before you can save 500k. Which means instead of borrowing and repaying and ending up with a house, you spend roughly that portion of your income on rent instead...
Oh, and "the rich" don't have "dibs on the freshly printed money" in the normal economy (arguably they do in a crypto economy because mining rigs aren't cheap...). The newly printed money is credit for people and companies not rich [or liquid] enough to have the cash to pay, and specifically it reduces the cost of borrowing because borrowers don't need to rely on rich people agreeing a fee to lend their money until it can be repaid.