[pas]

Central banks keep interest rate low not because of the stock market.

People focus too much on stocks. The real question is about the real economy, about price stability and unemployment. Especially in case of the Fed ( https://www.chicagofed.org/research/dual-mandate/dual-mandat... , but of course other central banks are also tracking labor markets too, even if de jure it's not their target - https://ideas.repec.org/p/fip/fedbsp/70.html ).

And we can say whatever we like about how the rich get richer, our current economic system do responds to what central banks do. Cheap money (an oversupply of low and even lower interest rate debt) helps persuade people to buy/invest/order things. It helps finance stimulus bills, and so on.

The savings are "just" an indicator. Sure, when the savings crash, the economy crashes too, but the causality is backwards. If/when the economy crashes (when industries stop, when people stop buying, when businesses let people go) savings will also become "worthless", because after all they represent future income, and if the economy tanks its productivity (income) tanks too.