To add to your argument about the incompetence of Monty, I have but one word:
CAEN
You're 110% correct. [ but you knew that ;-) ]
However, his incompetence there was so obvious I chose not to mention it.
(In the 'modern era', Monty was probably the 1st general officer protected by Political Correctness. He should have been fired at the least and at the most face a court martial, but Ike 'couldn't' do that.)