Agreed, with a caveat.
That caveat being that this is also correct.
Technically speaking, you can make almost any character in any medium function. You can have a mute protagonist in a novel, you can have a non-human protagonist in a video game, you can have a bloodthirsty psychopath as your protagonist in a movie. It's better to perceive it as a difficulty to execute, which is modified by the type of narrative you're entering. Playing as a bloodthirsty monster ala Joker in, say, a Romantic Comedy, wouldn't be appropriate in any context outside of bizarre shock humour. Meanwhile, playing in a story about a survival horror, a total monster of a character might just fit quite well!
Then, there's Nation RP's to consider too. The format allows each player to control a host of characters as opposed to any singular character, and having a methodical authoritarian in charge of an empire, or a bloodthirsty monster in charge of the military, can fit quite well there, and without any need to "force" it.
Ultimately, it's up to the skill of the player, and the cooperation of other players around them, and the type of narrative and conflict you're engaging with as to whether or not a particular character will work. In most narratives, I agree that the bloodthirsty Joker-esque anti-social mass murderer definitely doesn't work and I would turn it down immediately. In some narratives, though, it definitely not only works--but fits in such an appropriate way that it would almost hurt the narrative not to make one.
So, you know. Communication is key, as it always is, in ensuring that everyone is on board with the same general objectives and thematic goals in mind.