How to make Pure Evil Villains work

On sites like Twitter and Reddit it's become increasingly common over the years for people to discuss and debate storytelling with an increased level of enthusiasm. And, as a result, plenty of people like to talk about villains in things like movies, TV shows, and anime.

One common trend is for people to be automatically dismissive of pure evil/irredeemable villains, seeing them as 'lame' or 'uninteresting.' Personally I don't see it that way. And characters like Frieza from Dragon Ball, DC's Joker, or Big Jack Horner from Puss in Boots: The Last Wish make a compelling case for how engrossing such villains can be.

Music used:
Youthful Lunch - Persona 4
A Woman - Persona 5
Inkwell Hell - Cuphead
Freedom and Security - Persona 5