Flower Wars, as you note, get a lot of attention when Aztec warfare is discussed. It is important to note that the xochiyaoyotl were limited in not only when they were practiced, but against whom they were practiced. In the century or so the Aztecs were an independent power, they declared flower wars on exactly two opponents. Early on the Aztecs targeted Chalco., their most formidable opponent inside the Valley of Mexico. Later they arranged combats with the "transmontane states" of Huexotzinco, Atlixco, Tliliuhquitepec, Cholula, and Tlaxcala, the last of which would end up being their staunchest opposition. All of these groups shared a common cultural background with the Mexica, with the Tlaxcalans, Chalcans, and Huexotzinca also technically being "Aztecs," meaning they also traced their origins back to the mythical homeland of Aztlan.

Flower Wars were thus only waged against closely related groups who shared many aspects of the Aztec's cultural beliefs, including a emphasis on religious sacrifice of war captives. The fact that all early mentions of flower wars, including instances before the Aztec Triple Alliance even existed, involve Chalco may point to the practice being one specific to the groups that made up that complicated polity. There's unfortunately not really enough evidence to elevate this claim beyond speculation, but the fact remains that the Aztecs did not engage in flower wars against polities out their immediate cultural cousins. It's unclear whether the Purepecha, Mixtecs, or other non-Nahua, non-Chichimec groups would even participate in such an arrangement.

Military campaigns of expansion actually made up the majority of Aztec warfare. These could include shows of force to cow a town in to surrendering with little to no fight, pitched battles, coordinated invasions, and, yes, razing whole settlements to the ground.

Probably the best known example of the last practice involves the cities of Alahuitzlan and Oztoman. The latter had been an Aztec tributary but, along with Alahuiztlan, rebelled. In response, the Aztecs sent an army, promptly smashed the forces and fortifications of both cities, and killed every single adult. The children were then scattered among homes in Aztec cities, in a way that strongly implies they were sold off as slaves.

While it is true that few things enraged the Aztec state more than refusing to pay tribute, there was also a strategic aspect to the butchery (outside of simply intimidating other would-be rebels). The two cities were in the borderlands between the Aztecs and the Purepecha. After razing the cities, the Aztecs repopulated them with thousands of their own people. Oztoman ended up being an important fortress guarding that frontier.

Otzoman and Alahuitzlan were not the first time the Aztecs had decided to wipe out a city and replace it with their own people. Huaxyacac, modern day Oaxaca City, was one of the first targets of the Aztecs as they pushed into the Mixtec/Zapotec kingdoms of what are now the states of southern Guerrero and Oaxaca. Under Motecuhzoma Ilhuicamina, an Aztec army razed the city and several hundred Aztecs were sent to rebuild it. Subsequent campaigns in the region were able to use Huaxyacac as a launch point for pushing deeper into the region.

There are other instances of mass slaughter, but determining whether this was standard practice is stymied by the fact that most reports of Aztec conquests are little more than "in year X the Aztecs conquered Y." Some sources go into more narrative accounts, but it can be hard to tease the factual from the melodramatic in those sources. Duran, for example, writes that when Cuatzontlan and Xaltepec rebelled, the Aztec army found them so unprepared to resist reconquest that Motecuhzoma Xocoyotl ordered every person above the age of 50 killed. The justification was that elders are supposed to give society good advice, and the elders of those two provinces had clearly failed at that task and led the people into disastrous revolt. This could have happened, true, but Duran also has a flair for drama.

Seizing captives in battle was always an important part of the Aztec culture and military tradition. An Aztec army routed on the field, or fought to a standstill, is going to come home with more casualties than captives, just ask Axayacatl about the Tarascan campaign or Tizoc about Metztitlan. Glory in battle and sacrifices for the temples, however, was not the only driving force behind Aztec expansionism. They also want control of trade, access to luxury goods, and a steady supply of tribute flowing into the core Aztec cities. Simple smash and grab expeditions could not do that, so Aztec military excursions were strategic. They established friendly strongholds or setup garrisons from which they could resupply and conquer ever further and farther. Sometimes this meant the people at those strategic points needed to... go away.

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Some additional reading:

• Primary sources, the Codex Chimalpahin and Duran's History of the Indies of New Spain.

• Secondary sources, Hassig's Aztec Warfare and Hicks' article "'Flowery War' in Aztec History."