The more I think about it the less sense it makes: Though for a few hundred years in between the official residence of the Russian government was in saint Petersburg the Kremlin must have still kept it's symbol as a major seat of the imperial Russian government. During the reign of Nicholas II it must have been a hated symbol for many Muscovites. Not only was it a seat of power it also comprised five palaces which would represent the aristocracy that the communists were against and four cathedrals which represent the church which the communists were also against! Excuse me if my limited English is hampering the flow of the question but I am really wondering how the communist government found this a suitable seat of power instead of one of the massive constructivist buildings.
The move towards Moscow was a mixture of expediency and ideology for the Bolsheviks. The following is from an earlier answer of mine as to why Bolsheviks moved:
A. The foreign threat: the proximity of Petrograd to German, Finnish, or Baltic areas was too much of a security risk especially given the parlous state of the Red Army.
B. Infrastructure: Petrograd was not a self-sustaining city in wartime conditions. It was hard to supply grain to the city and this created the urban unrest that sparked the February Revolution. Additionally, the rail lines within Moscow and its factories were essential to maintain inner lines of communication during the Civil War.
C. Ideology: Moving to Moscow was congruent with a number of Bolshevik prerogatives. Unlike Petrograd, Moscow was the major industrial center of the tsarist state. Therefore it had the largest working class population and thus would be a suitable capital for Bolshevik state.
D. Politics: Although the Bolsheviks had gained much political ground within Petrograd, the urban politics of the imperial capital were constantly shifting. While the Bolsheviks had success in cultivating the support of the Petrograd Soviets, they never had full control over them. Moscow's support for the Bolsheviks was much more stable and less conditional than in Petrograd.
Using the Kremlin fit within the Bolshevik's rationale for relocation to Moscow. It was a preexisting structure which the Bolsheviks could use for an administrative center, plus the symbolism of a retaking this palace of the tsars in the name of the Russian people was an obvious boon for the Bolsheviks.
The Soviet Union's leadership did not intend to leave old tsarist Moscow intact. The palaces and especially its cathedrals became the sites of new monumental architecture that would symbolize the destruction of the old order and its replacement by a Soviet one. For example, the never built Palace of the Soviets was located on the demolished site of the Cathedral of Christ the Savior.
The problem was that the massive constructivist buildings intended to symbolize the new order were much too ambitious for the Soviet Union to accomplish in the 1930s. On the other hand, less ambitious socialist buildings (like the famous Stalinist wedding cake urban apartments) did get constructed and the destruction of cathedrals continued. The foundations for the Palace of the Soviets became one of the world's largest open air swimming pool, the Moskva Pool. The destruction from World War II and the growing self-confidence and Russocentrism of the post-Stalin leadership also meant that postwar Soviet urban design was less interested in obliterating the traces of old Russia. The result is the syncratic urban landscape of contemporary Moscow which eclectically jumbles architecture from multiple periods and ideologies.
Sources
Schlögel, Karl. Moscow. London: Reaktion, 2005.
Schlögel, Karl, and Rodney Livingstone. Moscow, 1937. Cambridge, UK: Polity, 2012.
