Surely a city that has suffered such extreme loss of population as Leningrad and under artillery bombardment should've been taken, why wasn't it?
German here, only got German sources, sorry. But might be interesting.
Initially, German scholars put the Leningrad siege in the same category as any other siege in the past. By starving out the defender, Leningrad would finally give in and save the siegeing party from heavy losses. And indeed, one of the reasons was to avoid Stalingrad-style urban combat against Red Army and Militia. However, Hitler's role was also emphasized, ordering a siege and exterminate the city because it was the center of the Russian Tzars as well as the start of the Bolshevik Movement.
More contemporary German history puts the siege into context with the other atrocities done by the Germans / the Wehrmacht in WW2. The Blitzkrieg had failed, causing the need to limit military operations and risks. Attacking Leningrad would require lots of those resources and possibly come with high losses and great risk. As a result of that, high military officials, instead of putting focus on limited resources making it not possible to attack Leningrad, made the extermination by starvation the official mission. Because of that, it can be put into one category with other genocidal acts during WW2.
tl;dr The siege and exterminating the population became the whole purpose of the operation after attempts to take the city were deemed to costly.
If you want to read a good novel on the matter, I recommend City of Thieves, by David Benioff (yes, the same guy who made Game of Thrones).
Hamburger Institut für Sozialforschung: Verbrechen der Wehrmacht – Dimensionen des Vernichtungskrieges 1941–1944.Hamburg 2002
Hamburg Institute of Social Sciene: Crimes of the Wehrmacht - Dimensions of the war of extermination 1941 - 1944
Jörg Ganzenmüller: Das belagerte Leningrad 1941 bis 1944. Die Stadt in den Strategien von Angreifern und Verteidigern. p. 13–82
Joerg Ganzenmueller: Besieged Leningrad 1941 - 1944 - The City in the strategies of attackers and defenders.
Follow up question if OP allows it. What would've happened to the war effort if they did manage to take it? Would it have been more than a blow to Soviet morale?