It was an incredible invasion that took a ton of planning and effort on everyone involved. Still one of the greatest military achievements of all time. It hastened the fall of the Nazis by at least a year and took some pressure of the Soviet front. Though strategically by 1944 the Soviets were well on their way to winning and the Western allies got way more than would be "fair" in proportion to Soviet causalities and everything. The desire not to see Stalinist Mainland Europe (hell based) did certainly encourage the allies to get moving by 1944. But honestly I don't think they were deliberately delaying or anything, it took a few years for the western allies to get their shit together to pull off a big invasion like that.