This really is one of the most interesting and consequential economic questions of our time. And I do imagine we will get an answer, because there is no political will to cut spending anymore.
The reason that all this stimulus hasn't affected measured inflation all that much is because the mechanism of monetary policy tends to be top-heavy, creating low interest rates which obviously benefits the rich more than the poor (people with high credit who tend to borrow larger sums more frequently). The rich channel this wealth into assets like real estate and equities, which are underrepresented in the CPI, in my opinion. There should be more of a "Volume Weighted" approach to balancing where large sums of the global economic market cap are sitting.
And since the rich can apparently just hold wealth in index funds indefinitely and cash out what they need for expenses (don't worry, if a pandemic freezes the economy, the Fed will rescue your position and create a new bull market!), few of those dollars creep into the economy. The "buy, hold, and never sell the entire market" philosophy creates economic distortion that enables this type of policy, and is incentivized by lower long term capital gains tax rates.
So by using this regressive, but fast acting, method of money printing, we can stave off hyperinflation and prolonged bear markets at the expense of increased income inequality. A more progressive, but slower acting way to finance government spending is to print a universal stimulus check, tax it, and spend the tax. We do both, but lean heavier toward the open market operations approach.
The hidden variable, not mentioned in this post: social security. Social security, which is due to become insolvent sometime in the next two decades, will have consequences like the progressive stimulus checks, but on a much greater scale, if the Fed starts printing money to finance it. This is where the "everything bubble" will convert into plain old inflation, when millions of everyday people are getting and spending cash that was printed out of thin air, assuming there isn't some sort of reckoning before that.