A general rise in the price level is what inflation
means and what it's always meant. Even under the quantity theory of money there isn't a one-to-one correspondence between prices and the money supply, because the velocity of money has changed. The Fed and the BoE tried targeting the money supply in the early 80s, and they were unable to control the inflation rate because the velocity jumped around.
We haven't seen hyperinflation in equities or real estate. Both are below their historical highs. Anyway, it's not "inflation" it's an asset bubble -- prices are too high given underlying cash flows. And if investors are so incompetent at investing that an increase in the money supply makes them immediately blow it at the casino, that's a strong argument that we can't trust markets to invest. The Austrian argument leads inexorably to an anti-Austrian conclusion. (I'm not convinced, but I'm not the one who thinks there's necessarily an asset bubble.)
Nobody thinks CPI is automatically the best guess of inflation -- it's just one attempt. Everyone knows that prices don't all go and up and down together, and we have to use a proxy. Anyway, the Fed doesn't use CPI. They use PCE deflator, and they only consider goods where price changes are more persistent (so called "core inflation").
The vast majority of fiat currencies have not experienced hyperinflation so far. In contrast, all gold standard currencies have gone off the gold standard, so the historical evidence points strongly towards fiat, not against.