I understand that the assassination of Kirov was what triggered the launch of the Great Purge and therefore, what allowed for Stalin to consolidate his power, but would there be something more important than this that allowed for Stalin to consolidate his power? Could it be that the assassination of Kirov was not necessarily that important in order for Stalin to consolidate his power as there were other, more important factors?
Stalin was biggest, but was not the only shark in the pool
The history of power struggles in USSR and other communist countries (China would be one example) is often murky and incomprehensible for the casual observer, especially the Western observer. You have many factions and cliques, and real differences between them are hard to comprehend. Those differences are sometimes ideological, sometimes ethnical, and sometimes there are power struggles between two or more groups based purely on "we against them" gang mentality. The whole situation is further obscured by the official party language, and conflicts resolving themselves, mostly on party congresses and conferences.
Anyway, Stalin was a leader of the centrist faction, a faction mostly comprising existing party functionaries interested in consolidating communist power in Soviet Union, and willing to put a brake on "World Revolution", at least for a time being. Theory of Socialism in One Country was their official doctrine in late 1920's and early 1930's. At that time Stalin's biggest opponents were the United Opposition (merger between the Left Opposition and the New Opposition), also known as the International or Jewish faction (leaders of the Left Opposition Trotsky, Kamenev and Zinoviev were all of Jewish ethnicity) . The Left Opposition was ideologically opposed to Stalin's views and demanded permanent global revolution. Ironically, the New Opposition (led by Kamenev and Zinoviev) was initially closer to Stalin's position but later relented and moved further to the left to be closer to their allies. With the help of the Right Opposition (sometimes called nationalistic, or Russian faction) led by Bukharin, Rykov and Tomsky, Stalin managed to marginalize Trotsky and his allies in the United Opposition by early 1930's. However, the alliance between Stalin and the Right Opposition was short lived - Stalin never planned to share power with them or to pursue their more liberal and market oriented ideas. Therefore, by the time of Kirov's assassination they too were marginalized and put aside. Stalin would use the Great Purge to get rid of them completely.
There was another group, potentially most dangerous in Stalin's eyes, and that was the Red Army itself and some of its more charismatic commanders like Mikhail Tukhachevsky. There are indications that Stalin wanted to remove Tukhachevsky as early as 1930, but could not do so because he was not sufficiently powerful at this time. What is certain is that Stalin feared a Napoleon like overthrow of revolutionary government by an ambitious general, and Tukhachevsky was certainly ambitious and sometimes called the "red Napoleon".
What about Sergei Kirov ? Kirov belonged to Stalin's centrist faction and was considered his friend and ally. He was not regarded as a potential opponent, and was politically one of the weakest members of Politburo, residing in Leningrad and not Moscow. However, there is a possibility that Kirov would oppose Stalin's excesses in dealing with his opponents within the party. If we accept the theory that Stalin organized his assassination, then Kirov could be regarded as a sacrificial pawn in Stalin's game of deadly chess. But even if we do not believe that Stalin ordered Kirov's death, he certainly used it to put in motion an already existing plan for purges.