The Rome-Aztec comparison is I think also useful. Both Roman and the Aztecs were massive, powerful empires with bigass legions which dominated, destroyed (physically or culturall) and bullied other cultures, but had remarkable achievements as well. Both killed insane numbers of people for insane reasons on the regular. The Romans, however, got us to all read their history, and understand their insane reasons, and our own culture attempted to convince us that all the bad things they did either weren't bad, actually (lol), or were tiny in comparison to the good. But with the Aztecs, there were the "other", and their culture was destroyed (intentionally), rather than taught to most schoolkids for centuries, so they just seem like terrifying weirdoes. I'm not saying either was good - both cultures, even when you understand them, were pretty psycho, but if you understand one and not the other...
I really don't think this is our culture's view of the bad things to do with Rome. I think there has always been a duality to our appreciation of Roman culture. Its impact and its achievements were significant, but its heavy use of slavery, its destruction of Carthage, its oppression of many different peoples, its use of violence for entertainment, its persecution of the Christians and its mistreatment of the Jews and their eventual diaspora, are all well known. but the victors weren't the Romans, they were not the ones who wrote the history. It was the Christians, who were persecuted by Rome, who wrote the history (at least in our predominantly in our culture). I have long been interested in Roman history. There are always different attitudes in a given decade about it, but there usually remains a critique of it as well. Rome can be used to invoke positive ideas about civilization but it can be used in the same breath to invoke ideas about decadence, cruelty and oppression. And I think it is significant that in a lot of media the Romans are the villains (not all, but a lot): especially films set in Judea. If you read books like Roman murder mysteries (there is a whole genre dedicated to this), the issue of slavery frequently comes up. Even something that seems very 'pro-Roman' like I, Claudius (which is an outstanding miniseries, and the book is great too), spends most of its attention on the bad things. Even in the golden age of Hollywood: you have films like Spartacus which are about a slave revolt (which ends with a massive crucifixion on the Appian Way: this is not an effort to say the bad things of the Roman empire were not all that bad).
I can't comment as much on Aztec stuff, as I mostly was interested in Mediterranean and Chinese history.