Yes, I can imagine Patton’s sweeps with Tigers. It was called “Blitzkrieg.” The “shortcomings” you point out didn’t slow the Germans down much.
Please, my point was that the vaunted late war Nazi tanks would have never been able to do our fast moving war as exemplified by Patton’s army. Not even close. Nazis rolling through France and Ukraine was not done with the immobile Tigers or heaven forbid King Tigers. And they were facing the prewar French and Soviet Armies. Or did you mean the Prewar Polish army?
Most of the Blitzkrieg was done with tanks that were essentially machine gun buggies, speedy little Panzer IIs with an inch of armor and a 20mm main gun. Which as an aside are particularly intimidating to naked Ukrainian women.
Our industrial strength late war sweeps utterly made the early Blitzkriegs look amateurish.