Not sure that was the reason, I've seen it convincingly argued both ways. I lean toward the idea that the Finnish government didn't want responsibility for Leningrad, nor the casualties that would come with taking it, so they hedged their bets and let the Germans get on with it themselves, while against Murmansk/the RR they couldn't really overcome the defenders due to the lack of logistics in the region; they needed Leningrad captured to have a RR link to the region with the Murmansk RR to be able to have strong enough forces to cut it. Without that it wasn't a lack of desire to deal with the RR or city, just the lack of means. It also didn't help that their German allies had little training or experience to fight in that environment, so in some ways it was the Winter War reversed thanks to the Soviets defending on top of their logistics.
To expound on this (and to refer to what I have written elsewhere): Mannerheim did not want an assault against Leningrad for practical military reasons and for diplomatic/political reasons both, and he managed to convince the government's "inner circle", first of all President Ryti, of this. In the conditions of the time in question (from late 1941 into 1942) the Finnish Army going against Leningrad would have meant high losses for the Finns, a lot of supplies and materiel expended, and major morale problems for the troops and the nation. The attack would have been very unpopular among most of the troops that would have been ordered to participate. And the then on top of that, even if the city was taken, things would not look any better: when Finland was practically dependent on Germany for feeding its own population in 1942, having to take responsibility for even a part of Leningrad's population could only mean a mass death scenario. The Finns could not feed the people of Leningrad, and they could hardly expect the Germans to feed those people for them. The huge national-level risks involved, in terms of supply and logistics, in the first instance, and in terms of diplomacy (towards both the Axis and the Allies), in the second, are obvious. The potential costs of the attack by far outweighed the potential gains in the short and medium term.
The Murmansk railway was a different question. An attack against the railway's functioning branch around Belomorsk would not involve many of the huge risks included in an attack against Leningrad. But then such an attack would also be very costly and difficult, it would require committing a lot of troops (suitable for operations in East Karelian wilderness conditions, which all Finnish units were not) and it would stretch the Finns' already extended lines of supply.
Finland itself had only limited gains from such an attack against the Murmansk railway, as well: it would essentially be an attack done to support the German war effort. The risks involved in that operation were comparatively more on the diplomatic/political side of the equation: what will the Soviets and the Western Allies think when Finland is now committed to actions that are not just connected to particular Finnish objectives ("a separate war for independent goals" was the official line the Finnish leaders and diplomats argued for, towards the Allies and the neutrals, to distance the nation from Germany and its goals, and rather successfully at that*) but are working for larger Axis goals as well. One big looming threat was always the US also declaring war against Finland like the British had. If there is less of a risk of the Americans going to war against Finland, an attack on the Murmansk railway would be comparatively more likely to be tried by the Finns.
But then again we come to the question if it could be done. The Finnish resources were limited, and like you mentioned, the Germans were next to useless for fighting in the conditions in question. For fighting in sub-Arctic wilderness, at any time of the year, the Soviets and Finns were probably the very best in the world at the time. The German troops, even their so-called mountain troops, continually proved unprepared and inept when operating north of Lake Ladoga. And, again, these conditions favoured the defender disproportionately. For an attack against the Murmansk railway, the Finns would need German support. But for a successful operation, that German support would better be material assistance, and, say, German units freeing up Finnish units from elsewhere rather than German units taking part in the attack itself. This calculation involves then a political risk as well: the more the Finns are dependent on German supply, and the more German units are needed to defend Finnish lines, the more leverage Hitler has over the Finnish government.
Unlike in most Axis nations, the Finnish government was one that was created democratically (even if in wartime conditions) and was made of politicians that had risen to their positions in prewar conditions, through mundane party politics. To understand the functioning of the Finnish government during the war, I think we need to think of it as not being committed to a "total war" in any real sense, not subscribing to a "destroy or be destroyed" mindset. The Finnish leadership's politics were not ideological or radical to the degree the Nazi, Soviet or even Western Allied wartime politics were. They were based on the understanding that Finland was a small nation in between great powers, with very limited resources and very limited freedom of action. Small nations don't decide great wars. They just try to look after their own interests the best they can, and they let the great powers duke it out between themselves, to decide who comes out on top - this was what the Finnish leaders were thinking, and it informed their decisions about the war.
Looked at with hindsight, the Finnish leadership's understanding of the situation was a combination of level-headed realism and some leftover naivety and wishful thinking conforming to interwar modes of thought. President Ryti et al. really thought that Finland would have the best chance to survive by hedging its bets, by giving neither the Axis or the Allies a reason to be particularly cross with Finland's actions during the war. In reality Hitler and Stalin needed no particular reason to destroy small nations, and the Western Allies could be very cold to countries in the wrong camp as well. But then when we think about the actions of the Finnish leadership during the war, and the likelibility of them committing to this or that military operation in support of German objectives, we need to remember that while Stalin and Hitler (and most Axis leaders besides) did not really worry about the death toll they would be subjecting their nations to, to reach their goals, or the diplomatic fallout of their actions, the Finnish leadership was acutely aware how little resources the nation had, how few losses Finland could sustain, and how precarious Finland's international position was. All potential actions would be viewed through a certain cost-benefit calculation in Helsinki (and Mikkeli, where Mannerheim's HQ was), a cost-benefit calculation unique to the Finns.
*The understanding that Finland had just limited objectives was also shared by the rank and file of the military, and also the majority of the civilian population. There was a lot of opposition among the troops already for crossing the 1920 border, and in some units this opposition nearly led to mutiny. In Väinö Linna's
The Unknown Soldier one character summarizes the popular view (my translation):
Rokka: "We don't care about Europe. We'll take Karelia. Then we can bloody well go home."