I am appalled by some of the suggestions made here, that warships are consumables, etc. The decks are not important, but MEN fight from those decks, you do not simply throw away thousands of lives, maybe tens of thousands, to attack into a bad location, which, even if you succeed, will mean NOTHING to the war's outcome.
From the beaches of Normandy it's about 600km to Germany proper which in OTL was very hard slogging. In Danish case the Germany proper, where the German war industry and the core of their ability to wage war was, would be much closer. A continuation landing to German coast will place Allied Armies within some 200km's to Nazi capital.
Every bomb dropped for interdiction is not falling upon some French farmer but upon German economic system, effectively combining the Allied tactical and strategic air effort to deadly efficiency it achieved in early 1945 already during summer of 1944.
The psychological effect of creating a free Germany much earlier, even if this means just, say, Schleswig-Holstein, is also significant and may mean yet faster end of the war.
Last but not least, one significant factor in delaying the Allied advance in OTL was that the logistical machinery was not capable of sustaining offensives farther than some 500-600km's from the SPOD until railways were repaired. In case of Danish operation this point is somewhere south of Hamburg (in Jutland option), in case of continuation landing on North German coast this line lies somewhere around Prague. Thus the Germans, after initial breakthrough, will not be able to rally like they did in OTL in September 1944, prolonging the war till May 1945.