Cash in the bank normally doesn't keep up. If it does, the orthodox view is that you risk a deflationary spiral.

Central banks want to incentivize investments.

This is a phenomenon of the last two decades. Before the fed started cutting rates after 9/11 (to support the country, the financial markets, the housing markets, etc.) both money market and savings accounts (you had to choose a good bank) usually gave positive inflation adjusted return.

Barely.

In real terms US bills have returned 0.4%/yr over the last 120+ years

Seems to me Treasury bills meaningfully outpace inflation, on average: https://www.bauer.uh.edu/rsusmel/other/lrret1.htm. But I was talking about cash accounts, which typically pay lower interest rates than T-bills or CDs (as noted on the above link).

In the late 1990s my savings account at the EmigrantDirect was paying about 7% with inflation around 3%.

This was not a term deposit, but a regular account, either itself with check-writing privileges or linked to a checking account with 1-3 day transfers. I think MMFs with check-writing paid similar interest, although not 100% sure as I never put my money there. Those were cash accounts as I could withdraw any amount, up to 100% of the account any time without any penalties.

It's not what they want. It's the mechanics of their business.

They borrow short at base rates and lend long at a margin

Owning shares in the entities for which money for goods and services pass through is the way to keep up with inflation. If I buy things from Costco/Apple/Toyota/Novartis/etc, then they increase prices, then their share prices go up accordingly.

Anything else will fall short.