The Italian campaign was sold (by the UK) as a way to grab 13 airfields in southern Italy, allowing long range bombers to hit the Romanian oilfields and various factories in Germany’s occupied areas. After that was achieved, there was no more nonsense about whether the Normandy invasion was a go.
The strain of supplying the allied troops on the European mainland was considerable. The Battle of the Bulge began as a German offensive (a hail mary, but regardless) that had as its objective the reduction of the port of Antwerp, to try to keep the allied armies in the west starving as it were.
A cousin who didn’t go through D-Day, but spent the better part of a year loading and firing artillery across France and Germany (including the Bulge), came ashore aboard an LST (Landing Ship, Tank; often derisively referred to as Large Slow Target). He got to talk to the pilot, who said a lot of pilots didn’t actually beach the craft, making unloading difficult or delayed. There was a liquid ballast which got pumped to the rear, which raised the nose a bit, allowing dry disembarking through the big door up front. After unloading (which could take hours), more liquid was pumped to the rear, raising the bow, and allowing the LST to back off the shore. Once clear, the ballast was rebalanced and the LST turned for home and another load.