The shutting off bit makes me think that Pi actually is overheating.
While similar comments on how the Pi 4B throttles for heat management have been reported before, the number of reports indicate additional information: the temperature of the Pi owners.
Having said this, I have my 4B mounted vertically to a piece of wood and have yet to see problems, even when a fan is not blowing on it. I think there must be some variations in the shipped product.
Is the voltage fed to the SOC in each Pi somehow tuned to the individual voltage requirements of each particular part?