The war was probably indeed lost as soon as Barbarosa failed its objective. But had the Allies sat back, more casulaties on the Soviet side would have occurred. And there was the power balance "after the war." Sometimes politicians have to make decisions too quickly. The Russified western Europe might have been one their minds.
My uncle was in the second wave at Juno. He didn't talk too much about his war activities, but one Christmas, with a little whiskey, he opened up. His theory was that D-Day was called because too many American and Canadian young men were in English causing all sorts of trouble. Part of the reason for June 6 was to get them out of the country.