I don't recall having a single immigrant professor at any of my schools except one Hungarian refugee who was a right wing fanatic, and I liked him.
The ability to teach, imo is more inborn than learned. Sort of like being a sprinter. You can improve a little but you can't put in what God left out.
Back in the early 80s at Texas A&M, many of our professors were foreign. Some had such thick accents, I couldn't understand a thing. I was first a Chemical Engineering major, and it was full of foreign profs. Then I switched to Computer Science, and it didn't have many foreign profs. I also did much better in Computer Science.