This theory was put to the test between 2007 and 2019, where the Fed greatly increased the monetary base during and after the financial crisis. As it turns out, the velocity of base money was much more flexible than assumed, and the monetary base remained greatly increased (about 4x its pre-recession level) without excess inflation.
In comparison, the covid-related increase to the monetary base has been less than a doubling (see https://fred.stlouisfed.org/series/BOGMBASE).
> I personally envision 5 to 7% inflation when things return to normal in the US (so schoolyear 2021-2022)
If you really think that, then go to a broker, buy TIPS (inflation-protected securities), and go short nominal bonds of equivalent duration. The five-year breakeven inflation rate (US) predicted from these bonds is about 2.5% (https://fred.stlouisfed.org/series/T5YIE), so if your views are correct you would make a mint.