You should see what happens when you say something bad about the Bren.
You won't see me do that, I love the little bugger ...
In the World at War documentary, if memory serves, an American officer said that the reason Falaise wasn't more effective was because the Canadians/British weren't quick enough, and the French didn't do a good enough job of clearing the area for the US.
Actually, the French, aka Leclerc's
2e DB, "hijacked" a road earmarked for one its neighbor divisions in order to move faster itself. The move had good and bad consequences in the capture of the next city (I can't recall which one) and has been the matter of many debates since. Another consequence was that the French, being up front of their (American) corps because of this act of indiscipline, received the mission to capture Argentan and give hand to the British coming the other way, hence closing the Falaise pocket. The DB did enter Argentan (Wolverines & Fusiliers-Marins leading the way) and fought in the city, securing half of it. But the British/Canadians never came, and the French battlegroup wasn't strong enough to stand in the way of two retreating German armies and had to contend themselves with holding what they had and taking potshots at the retreating Germans.
This first opportunity to close the pocket on the Germans was lost, leading to the Poles & Americans doing the job at Chambois a few days later, and a lone Polish battlegroup at Mont Ormel taking the full brunt of the two German armies trying to break out.
I also recall an American officer saying that the Anglo-Canadian advance wasn't quick because they moved at a much slower pace than the American advance in order to prevent casualties, while the Americans could advance much less cautiously "because [they] could afford the losses".
That's actually very true.
Britain was running out of soldiers, especially infantry replacements. At the beginning of the Normandy campaign, the average American soldiers was 5-6 years younger than its British counterparts, for the latter had been scrapping all the reserve, including heads of families. After one month of combat, Monty was warned that infantry casualties couldn't be replaced anymore, hence the decision to plan Goodwood as a sole armored assault with the 7th, 11th & Guards Armoured Division charging without proper infantry support. Tanks could be replaced, but infantrymen couldn't.
Remember that Britain had to feed men to armies deployed in France, Italy & Asia, just like the USA, but with a population 10 times smaller (at best) while being at war for 5 years already!