It is true that Norway may seem to be defensible, but you also have to take into account some other factors. First, under air superiority transfer of reserves by Germans would be extremely difficult due to necessity of transferring troops by sea. German naval forces were extremely weak by 1944, so Soviet Northern Fleet - without even taking Western Allied assistance to the account - would have naval superiority. A narrow front does not mean it's a defensible front as the narrow front could be easily outflanked, assisted preferably by strong Soviet paratroop forces. Comparison to Finland is not relevant, as due to geography the possibilities of using paratroops in Finland were much smaller. Soviets had much more experience and also more success in amphibious warfare than Germans, one has to remember.
One also has to remember that after taking Narvik the Soviet forces could be supplied through Sweden via Luleå-Narvik railroad.
One ATL where the Soviet invasion of Norway would assist Western Allies greatly would be one in which a deal would be made between Soviet Union and Western Allies that the Soviet invasion would begin in May 1944 - before Operation Overlord - to distract German attention towards Norway.
This would ensure numerous benefits from Western Allied operational and Soviet strategic viewpoints. First, some German reinforcements might be lured to Norway. Second, remnants of German Navy might be lured into battle. Third, German 20th Army in Finland would be isolated after Finland was separated from the war, as Finnish and Soviet navies would block the Baltic supply route. There would be ample time available for an Arctic campaign, and Soviet air power would be extremely effective due to period of no night at all. After getting Finland out of the war the resupply of forces would be easier as it would be carried out through Bay of Bothnia.
The best case, from Soviet point of view, might be a frontline in Trondheim -level before winter of 1944-1945 sets in. Final campaign in Spring 1945 might see Swedish participation.
The interesting part would be, naturally, the post-war -future. Norway might well continue it's prewar neutrality, perhaps forming a part of the Scandinavian Military Alliance proposed during late 1940's in OTL.
What? While the E6 might be a road, it is easily sabotaged to become no road at all, especially if you just sink the ferry at the multiple locations where it crosses a Fjord. The single real road is easily and almost permanently sabotaged, as is port installations. While the ports are very good, they were small commercial ports, there'll be no heavy duty cranes to offload things like ammunition, artillery, heavy weapons and other supplies. Add some German destruction and every port is practically worthless to supply a modern army.
The 1½ battalions of the Norweigan Police Brigades (in reality trained and equipped like Swedish regular infantry, plus PIATs courtesy of the British) had problems keeping themselves and the small civilian population supplied in northern Norway, despite ample support by Sweden, including an American air bridge from Luleå. How are you going to supply Soviet forces that can take on two German divisions (and the divisions of the 20. Gebrigsarmee had suffered much less than other divisions and were at 80-90% of authorised strength and still high-quality, compared to other divisions on the eastern front) head on?
Sweden would NOT be happy about a Soviet presence at the border and would not like to see the German occupation of Norway replaced by a Soviet one - Russia is after all the old arch-enemy of Sweden. I seriously doubt that Sweden would allow the Soviets to send supplies along the Luleå-Narvik railroad. When the Germans were allowed, June 1940-August 1943, it was because Sweden was weak and Germany strong - strong old cultural and military ties helped too, something the Soviets did not benefit from. Sweden letting the Soviets use their railway network to supply troops occupying Norway is pure ASB.
The Soviet northern fleet was even weaker than its German counterpart - by late 1944, most of what remained of the Kriegsmarine was in Norweigan waters. The Soviet Northern Fleet undertook no operations far from its bases and most of its personell died fighting as Marine Brigades on land. British ships delivered as compensation for Italian ships were never really put in running order. Besides, the Soviets did not have a very good track record with landings - the few they did all went badly. And it is very easy to mine a fjord.
How would the Soviets be able to invade Norway BEFORE knocking Finland out of the war? Remember Petsamo? You dont do a Norweigan advance when there's Finnish and German forces that can retake Petsamo, cut you off and put you between a hammer and an anvil, stuck in the worst terrain of Europe. Finland was alive and kicking until September 1944 and the Soviets had lots of forces tied up against the Finnish army and the 20. Gebirgsarmee in northern Finland. The western allies were investing all their resources into Operation Overlord at the time and both them and the Soviets were quite happy about the German forces in Norway, which were more or less locked there since Sweden cancelled the transition treaty in August 1943 - small numbers of men (mostly specialists) could be moved by fast boats during nighttime or by air, but large srategical movements were impossible. That was why there still was almost 500 000 Germans in Norway in May 1945 (although most of the troops were low-quality fixed defence units without operational mobility).
A Soviet invasion of Norway really only helps in the sense that it distracts the western allies from France (if they are to lend a hand) and distracts about 100-150 000 Soviets (and especially a HUGE logistical apparatus, which is even more important) from the post-Bagration advance and knocking Romania out of the war.
20. Gebirgsarmee would not be isolated either - it was supplied from depots in northern Finland, depots that were supplied from Germany by ship.