Stalin had more than a key administrative role (one that basically gave him most of the power in the country since April 1922), he was also generally liked and admired by a fair chunk of his peers and his theoretical work (very important in the Bolshevik party) was well respected.
Stalin was a middling theoretician at best. His only work of note was on the National Question and he basically wrote that with Bukharin's help with the general details already laid out by Lenin - in fact, a lot of his theoretical contributions were co-written with Bukharin.
Stalin gained an administrative position of power earlier than 1922, he became head of the Uchraspred, the Account and Assignment Section, in 1920. According to Merle Fainsod, the Uchraspred "concentrated first on filling party posts. Appointments to the highest party positions came under the jurisdiction of the Orgbureau.... The Uchraspred rapidly extended its control down through the guberniya or provincial level. By the beginning of 1923 its controls reached the uezd, or county level. The report of the Uchraspred to the Twelfth Party Congress in April 1923 indicated that more than ten thousand assignments had been made in the preceding year. Stalin, in his organizational report to the congress, made no effort to conceal the range of Uchraspred's activities; indeed, he revealed that it was expanding its jurisdiction into the state apparatus." This coupled with becoming General Secretary in 1922 and his ally Kaganovich becoming head of the Orgbureau basically meant that all throughout the early 1920's Stalin had control over delegates to party congresses, appointments to positions of power, and he could transfer his political enemies to distant posts away from the centres of authority. Sverdlov surviving the flu, Krestinsky keeping his General Secretary role, or just some other individual with a few more scruples getting such an important role could have changed the party political make-up immensely.
And perhaps most critical of all, while other Politburo members were sorta interested in limiting Stalin's power, they were also keen to keep him in his job. When Stalin attempted to resign (no less than three times between 1925 and 1927) his resignation was refused by the rest of the Politburo.
I'm also not entirely convinced that this shows that Stalin is in any way particularly different from other members of the Politburo. Lenin threatened to resign multiple times and was often refused. Trotsky offered to resign over Brest-Litovsk if it would have made the negotiations go better and Lenin refused him. Zinoviev and Kamenev both resigned and soon assumed their positions again. Other Bolshevik leaders threatened to resign or did resign over one political situation or another and were consequently re-elected back into their roles. I don't think it marks Stalin as unique, is what I'm trying to say. It was a political move to try and emphasise a position. One interesting point is that the Left-SRs, when in government with the Bolsheviks, used the threat of resignation to get the Bolsheviks to moderate their positions.