This problem is older and existed already before the pandemic, but instead of Polish plates it was German/French, as those countries didn't have such expensive insurance and it was easy to have a foreign branch of a company register one's company car.
The first crackdown was also before the pandemic and being Polish and in-and-out of Italy I fully expected to get caught in the crossfire, but that never happened.
Apparently I was driving too much like a tourist - indicators and all.
That being said a few people from the local Polish community got into trouble, but it always first due to driving into a Zona a Traffico Limitato with a car that shouldn't be there - plates notwithstanding.