They did but not without challenges.
There were a lot of things they could have done differently  Â
Explanation:
Lets take a look at the background again.
The Aztec (who called themselves the Mexica) were originally a small nomadic group, but their warrior culture enabled them to grow and eventually dominate their neighbors. They established an empire that in time encompassed south and central Mexico. The Aztec eventually dominated 400–500 city-states and over 5,000,000 people. They did not directly govern these other city-states directly, instead, they established a tribute system.
This tribute system along with taxation was the main source of income for the empire.Tribute was collected as a collaborative effort by the members of the Triple Alliance every 80 days, 6 months, or 12 months, depending on the goods being collected and the distance that they had to travel. Tribute items typically included warrior costumes and shields, tropical feathers, copal incense, paper, foodstuffs, and animal products. Official tribute collectors, known as calpixque, were located in each of the conquered provinces and ensured that payments were made as required. According to history, tribute payments were generally reasonable, and were only increased if a region reneged on its tribute obligations. Regions that failed to pay tribute were severely punished.
So where did they get it wrong?
The Aztec Empire was similar to a union of city-states.
A city-state is a usually small, independent country consisting of a single city, the government of which exercises full sovereignty or control over itself and all territories within its borders.
This lack of centralized organization, along with the tribute system and the fear that the Aztec engendered among their subjects, created a great hatred of the Aztec. The Spanish were able to capitalize on this hatred when they set out to control the Aztec Empire in the early 1500s.
What changes would have improved the system?
At that time, they probably could have done nothing. But given the benefit of hindsight, it is clear now that besides creating a centralised system of governance and collection of tributes, which was safe for the calpixque, Aztec  could have managed it's reputation for huge human sacrifices, a practice which engendered fear and stirred a rebellion among the city-states.
Cheers!
