It was not necessary. The threat of a landing would have been enough to keep German troops in France. Not landong in France would have given the chance to conquer Germany without fighting all its armies.
Pushing through Italy was not the alternative. Plan B was to land in Yugoslavia and the march towards Poland. That was Churchill's idea. It would have met only weak German forces, taken the full strength of allied navies, cut off German Ostfront and liberated Middle Europe.

The advantages of D Day was that France was liberated earlier and the England did not have to suffer from German attacks that much. Also the backbone of the German airforce was broken. German submarines did not matter much after the landing.

Quote Originally Posted by IliaDN
But loses were terrible ... were they?
Losses were not high, ar least on the allied side. They lost a lot at the landinmg, but in total the losses were much less than at a comparable operation of the Red Army.
German losses were desastrous, of course.