It seems to me like it would be easier for the Allies to supply a landing force there and open a new front like Stalin wanted than France where they were relatively close to the heart of Nazi-occupied Europe. Since as I understand Norway provided a lot of ore that was needed for the war effort it would be a worthwhile place to retake and it would be good for launching shorter range bombing runs on Berlin and such. Also I would imagine since the Reich had to use it's relatively small fleet to move soldiers and material back and forth that Allied submarines would have relative ease cutting their supply lines.
Air Support and Landing Craft.
These two factors were the primary strategic constraints that dictated what the Allies could or could not accomplish in WWII.
Norway is outside of the radius of all but the longest range fighters based out of Britain in WWII. See this graphic Only the longest range allied fighters and carrier aircraft could have reached Norway, while the German airforce could have maximized their response to any landing. This constraint basically restricting landing operations to a fairly small area of Northern France or places in the Mediterranean within reach of land-based air.
The other big constraint was Landing Craft. While the USA had been mass producing landing craft at unprecedented rates since early 1942, they were a very serious pinch point for allied logistics. Norway is quite far from England in comparison to France and without capturing a port it would have taken several times as many landing craft per combat division to supply troops in Norway. The invasions in France had considerable difficulty in securing enough ports and the Normandy beaches were still receiving supplies over their artificial harbors and beaches into late 1944 early 1945.
Lastly, you're under the wrong impression about Allied submarines being able to effectively operate in the Baltic or the Norway-Denmark strait. Mines, shallow water, and aircraft made British submarine losses in this area unacceptable in 1940, and operations had to be curtailed.
Finally, Norway was useful to the Allies even while German occupied due to deception operations. Operation Fortitude North and a host of other deception operations pinned down as many as 13-18 German divisions in Norway where they contributed very little to the war effort. By contrast the western front faced 60-70 German division, and the Italian front 20-28. So the Allies were able to basically use up German resources in Norway in 1944-45 without actually committing ground troops, landing craft, or air assets.
By the time these factors were no longer important, Allied forces were already pushing into German territory, and the end of the war was a matter of months.
One part of the reason is that i stretched already thinning German resources even thinner. Germany wanted to keep control of the country and due to the threat of invasion had to station troops there that could hold out in case that invasion came. At the same time it cost the Allies little to just maintain the apparent imminent invasion to keep the Germans in place.
Norway was as you pointed out a strategic location to control due to the Swedish iron ore being exported out of the port of Narvik. There are more reasons that made it valuable to the Germans like the submarine docks they constructed and the heavy water plant (a vital component to the nuclear program). These and more are reason as to why Germany would want to keep Norway.
What would the Allies gain by invading Norway? The population would be grateful but on the strategic level is Norway of little importance to the Allies. They don't really need the iron and have a more advanced nuclear program going on in the US already. Norway mostly only connects to Sweden and Sweden is neutral so no big advantage in geography can be gained. The mountainous terrain favours defenders in most cases so any attempt would probably bog down to a war of attrition. Not really the type of war you want for a target with low importance.
What the Allies did instead was to include Norway in various plans that were never meant to be carried out. Like Operation Bodyguard that was meant to pull German attention away from Normandy on June 6, 1944. Several places were slated for invasion under those plans including Calais and Norway. The effect on Germany was that several hundred thousand men were kept in Norway and therefore out of the war. With deception and false information did the allies effectively neutralise a good portion of the German army to little or no cost to them self. Norway could not really provide anything the Allies either didn't already have or needed. France is more developed when it comes to airfields and closer to the German industrial heartland in the Rhine valley. Looking at it this way makes any invasion of Norway just a waste of lives.