Bradley despised Montgomery and lost his command because of it.
Bradley was also contemptuous of Patton as well. In his third volume on World War II, Rick Atkinson talks about all the U.S. senior commanders in Europe and the reality is that they weren't an outstanding group of individuals. Between the personality issues and the army commanders in over their head and the political give and take it probably added immensely to the casualties.
Eisenhower despised Montgomery as did Patton as did Bradley as did just about every American commander. Ultimately, especially after Market Garden, Eisenhower had enough and put it on the line to Churchill, either Monty goes or he goes. Churchill was ready to cut Monty loose. Monty got wind of it and got on his knees asking for Ike’s forgiveness. This was a blow to Monty’s ego who went on, post war, to ravage Ike as a poor choice for CINC because he had never held a battlefield command.
Anyway, the entire way Monty had to be handled with kid gloves it is yet another classic lesson of what happens when politics and military planning mix. In short, they don’t.