The secret is that those $100 should have never been put into the bank account in the first place. Investing the same $100 into the S&P500 would have yielded you $190 as of today.
Despite the lack of financial education, there's a distinction that needs to be made. Investing is not the equivalent to saving. Savings are supposed to be stored in the least risky financial instrument. When you invest $100 in S&P500, you realize that this is an intentional decision, in which you understand that you can lose money. There are no free gains. There's a tangible risk, it's just that the S&P is less risky than other investments.
I would highly doubt that the S&P beats real inflation often. It was around $3000 in mid 2020, it's around $6000 now. In this particular case, if you invested four years ago, you'd have most likely beat real inflation, but if you check the numbers for previous years, you'll notice that it barely touches it, and frequently loses; you'd have to put that money for an indefinite time to actually beat inflation.
But I'd argue that's not a problem of inflation in itself. If new money would enter circulation from the bottom up, say via UBI, the Cantillon effect could be largely circumvented. But of course there's no profit in that so the incentives to implement such a system at a scale is pretty much nil.
UBI would have similar consequences to lowered interest rates or to subsidies. It'd be a matter of time prices would rise, and then the UBI would not "be enough".