My thoughts on this are that a good villian isn't relateable at all and is iredeemable. Someone who you want to punch every time you see them, and can't wait to see them get fucked up. But that's not the ONLY option.
Sometimes a good villian can be a Hannibal Lectar type, who is relateable to a degree, but still not in any way good. The kind of guy who steals the show, and you want him to win, but he's still not a good person and gets no redemption. And that's fine.
Depending on the plot, a villian can be redeemed, but it really has to play into the content and context of the plot well. Like, I don't want Hannibal redeemed, because that's totally out of character. But Vegita in DBZ worked, because of his life and what Frieza did (yes, I'm using DBZ as an example. Fuck off). His father was murdered, his race was exterminated and he was raised by a genocidal alien narcisist to be a killing machine who singlehandedly conquered worlds, or got punished for not doing so.
He was a villian because he was a dick, but mostly because he had to be. So his redemption, coming in stages over time, worked out quite well and made him more likeable and memorable. Without that, he stayed a fight of the week, more or less. So his redemption both enriched his character and the story in general.
Its all relitive.
One of my favorite baddies was Zod from MoS, because I fully understood and sympathised with where he was coming from and why, but knew that he had to be stopped all the same. He was very compelling, and redemption wasn't possible for him. Not because he was so bad, but moreso because of the fact that he KNEW he was right, and from his perspective, he was. So how do you redeem that? You can't, unless his entire personality changes. And I think that alone is the best example of why the OP's image is correct.