You had me in agreement until the last few lines where you stated that Lee should not be included a list of great American generals, then you ticked-off Patton, Pershing, Grant & Washington.
I would take Patton off that list. My reason is that Patton did not command at the same level as the others mentioned. Pershing, Grant, Washington & Lee were all either theater commanders or Generals-in-Chief, Patton commanded a single field army. He did it well, but history is loaded with examples of generals who were superb at one level and disasters at the next. We can only guess how good Patton may have been.
All started as small unit commanders. Each had qualities and deficiences.
Washington made many tactical errors before he had the right kind of army to fight the revolution. Grant, made a lot of mistakes that cost him men needlessly. Wilderness and Cold Harbor just to name two. Pershing chased Villa all over northern Mexico handcuffed by BOTH US and Mexican governments.(even though Villa was recovering from wounds near Agua Caliente the whole time)
Patton was not only an aide to Pershing in Mexico, but found his future in Europe during WW1 commanding 1st Tank Brigade. His theories on armor tactics as a deep thrusting weapon in place of horse cavalry and the saber was as novel a concept as the laser is to weaponry now. And he carried the notion a soldier should LOOK like a soldier, from dress and decorum, from Pershing.
What got Patton in trouble was his mouth. He said what a LOT of officers only thought. He was a soldier, not a politician, and he only knew one way to fight. The Germans feared him, his men loved him, because he loved them. He was the most dangerous general we have ever had. He didn't make very many mistakes, the race to Messina was one, needless losses at Palermo just to beat Monty to get there.