Should the ultimate villian also secretly struggle internally? A sociopath often does have a pained inner struggle. Psychopaths get the free ticket to not caring but they're technically terms no longer used in diagnosis and they're considered on the same spectrum now, so maybe it's a sliding scale or different for every person who has this.
If we're speaking all cases, I don't know. What's the purpose of the villain? This is probably the better question for a thread, heh.
If we're talking about my own personal vision of "ultimate villain," then I think those whose actions cannot be well understood—because their motivations are hidden, absurd, illogical to extreme degree—are the most terrifying. We're verging on the idea of monster here. You know how monsters that are hidden are the most terrifying? That sort of thing.
Does such a villain make for a good character? Probably, yes, but not as a point of view character. Presenting POV sections might intensify the effectiveness of the villain, but this doesn't mean this villain is a good POV character. If you want to follow a villain around, make him a good POV character, you'll probably need that internal struggle and lots of other things besides.