Just a layman, but it seems to me that full employment is essentially achieved when the number of unemployed persons per job opening is less than 1. For the reasons you mentioned, actual full employment is unattainable. But even with inevitable mix issues, when the unemployed are outnumbered by job openings, I call that close enough. BTW, for a couple years prior to the pandemic, this ratio was below 1 in the US.
I don't think you wait for it to "kick in" and then take politically-unpopular corrective action. Instead you carefully measure slack, which provides guidance as to how much additional stimulus the economy can safely absorb without creating inflationary concerns. When corrective action *is* needed to combat inflation, there are always the conventional Fed mechanisms such as raising short-term interest rates, increasing reserve requirements, and selling government bonds. It's not limited to tough political choices like raising taxes or cutting government spending.
The larger point here is that MMTers seem to suggest that the US has not been aggressive enough in utilizing slack due to a fixation on deficits/debt, which they contend is the incorrect metric for affordability. This has resulted in a slower advancement of our standard of living than would have otherwise been possible. It also contributes to many of the social issues and costs associated with the unemployed.
As I posted before, I see MMT as more of a description of what we already have today as opposed to some radical new theory of economics. They just want different behavior and thus offer a different perspective. Specifically, they want fewer spending bills killed because of the CBO's traditional impact assessment. For example, we've been talking about infrastructure since 2009 and practically no one is opposed. Yet despite plenty of slack in the years after 2009, nothing was passed because of this fixation on offsets. Meanwhile we have chronically unemployed people in the rust belt and Appalachia who could have been rebuilding our dams and bridges instead of getting hooked on opioids. That's the argument in a nutshell, as I understand it.
