In practice, that is not happening right now, because the market for interest-rate-determining instruments (like Treasury bonds) is saturated by people who by and large don't care about making up for inflation in the return: the Federal Reserve, exchange-rate-manipulating foreign central banks (like China), and insurance companies.

You're missing my point. What you're saying translates to: "In theory, real interest rates are positive, but in reality they've been driven to negative levels because savings are so high." But nothing in theory stops real rates from being negative at any point in time.

By the way, your list of actors seems misguided: (1) The Fed buys Treasury bills when they issue cash, which is basically exchanging one government liability for another: it doesn't change aggregate saving. (2) Insurance companies invest money on behalf of people who buy long-term instruments such as life policies and annuities. (3) China does manipulate exchange rates, but the only reason they are able to buy so many Treasuries is Chinese workers saving large portions of their income and depositing them in the local bank. AFAICT, there is no case for giving any less consideration to Chinese workers than to US-based savers.