Monty also had a habit of assigning nasty jobs to non-UK forces under his command, such as clearing the Scheldt to the Canadians and as we are just now seeing, the Ruhr to the U.S. Ninth Army.
Using the Dominion forces to do the nasty jobs was an Imperial tradition dating back to the First World War. And the Dominions were keenly aware of it. I suspect it was one of the reasons for the recent Canadian draft riots.