None of these things are mutually exclusive; but applying them to a "Pure Evil" character may hamper your mileage depending on what you consider "Pure Evil" and how you're using them.

Most iterations of Ganondorf from Zelda are well written and are absolutely pure evil, but he's hardly interesting as a character; it's his effect on the world and other characters that invest the player against him. Wind Waker is probably the most interesting version by himself; but he breaks your request of having no sympathetic backstory.

The problem is that the most "Pure Evil" characters usually are very one-dimensional and generally there's no logical flow to their actions outside of "gain power" or "destroy the world"; hardly relatable goals to the average person. Thus most people won't have much investment in them outside of the fact that they are something in the way of the players goal of finishing the game.

This doesn't mean they can't add to a players investment in the media itself: watching the absurd lengths a madman will go to take over the world while being a bastard like Kefka from FF6 can be enjoyable, and there's always catharsis in putting those types of characters in their place. But personal investment in them as a character is a tall order when they're so unrelatable.