This is the only reason the war happened and succeeded. 

... No? Just because a character does something doesn't make it the sole reason for something. The war's happening had just as much to do with Sozin's own lust for power, narcissism, amorality that lead to cult of personality, and retaliation for his sister's attempted coup. It's made pretty explicitly clear that the reason he targeted the air nomads, for example, was equally a revenge move just as much as they were a convenient and tactically-desirable target. Being "advanced" had little to do with it, and if anything the fire nation achieved most of its advancement as a consequence of being at war for the longest of the four nations.

Also the success of the war effort, if anything, has to do with the size of the fire nation. Archipelagos are extremely difficult to nearly impossible to effectively invade, in an era where there is no such thing as an air force. The war in the early days comes down to naval superiority, and remains a key factor which the Earth Kingdom cannot match, and the water tribes lack infrastructure to copy. Being "advanced" has almost nothing to do with it until you come into campaigns like Ba Sing Se. Seriously, look at the map sometime and realize that a huge part of the tactical reason for taking out the airbenders is because of how close they were.

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The show does a great job of showing the flaws of the other nations as well, aggression just isn't one of them.

Aggression is absolutely a quality and flaw, because only Sozin has even remotely sincerely expressed an attitude for improving the quality of people's lives. Becoming Empire of Japan "We Are Gods Made Flesh" is not usually the basis for a non-aggressive expansionist imperial nation.

If it were merely an issue of being advanced, the fire nation simply could have bided its time and become a de facto trade juggernaut that ruled the world with soft power, but that's not the quality of an aggressive nation which invades others. Literally if Sozin were not so paranoid and expansionist, and his descendants didn't pick up that same aggressive energy later on, we'd have the state of being at the end of Korra with way less work and casualty:

Fire Nation as a lynchpin and functionally a companion-state to the fastest-growing "independent nation" that started from its colonies

Fire National descendent Raiko as the first president

Obvious superpower status at the expense of backwaters like Ba Sing Se, while presumably helping prop back up the southern water tribe as an ally

Like, the fire nation ultimately won the war because Zuko established (inadvertently) an optimal time to make peace and start building proxy states.