Many gods were monsters in a more casual sense.
I'm more confused why "monster" has to be something you fight. That seems a narrow definition, particularly given just...what mythology is. That makes an awful lot of very mythically-resonant creatures "not monsters" because they're either friendly or merely aloof. The Tarrasque, or rather tarasque in the original French, for example, wouldn't be a monster by that definition because it was tamed by a Christian saint (St. Martha) and only died because the city instantly opened fire on the creature as St. Martha led it back to town.
That doesn't really jive with most of the stuff I've seen from official modules, including some people decry as being "for kids."
It certainly doesn't stop us from writing such characters. Which I have. To great effect. My players very much enjoy hating some of my villainous NPCs.
Well...that's sort of the problem, isn't it? The bolded bit, I mean. Treating people not like other people is one of the key problems humanity has been dealing with since...well, at least the dawn of recorded history and probably for as long as there have been things we could even vaguely call "people." Treating people as non-people because of their physical appearance, or location of origin, or the language they speak, or the contents of their trousers, or the contents of the trousers of those with whom they share their bed, or what things they hold sacred, or...
Having creatures that are genuinely people, and yet also "monsters by form" is becoming difficult to accept now. Particularly because the odds are quite high now that someone in your gaming group either has one of the aforementioned benign traits previously labelled as a "monster by form" trait in the past, or someone they love/care about does. We're starting to see that it's disrespectful, all too often specifically to someone actually playing at your own table.