Altogether this is a very deep question. I'll do my best to summarize what I know villains are for:
A villain(s) upsets a content or peaceful situation. The hero(es), must reset the situation, and learn something along the way.
The redemption of villains is a very, very risky idea. Villains needs to be defeated, because a villain is supposed to represent chaos and disorder, so much so we instinctively want it gone, like an infection. Villains make the story 'sick', and the heroes are the doctors.
Do you want to make friends with your mucus? No, you want it gone. When the villain is defeated, the story is (supposed) to be over.
Redemption is a universal desire, I think we all understand that. But I think we also somehow require that redemption be deserved somehow - it should be more than just given...it needs to be earned through trial and fire - ie - the villain must, rather unintentionally, become heroic by realizing their intrinsic worth.
Starlight is an interesting situation. She was presented as redeemable from the outset (she's cute!). So I think Starlight's story is a decent example of the problem (the villain) being somewhat disembodied (an evil ideal) from the subject (Starlight herself). She just had to realize her hypocrisy and pay for it with humiliation. And now, she serves her 'penance' as a student of Twilight. IMO, a very endearing and nicely done scenario.
So to answer the question more directly - villains should be interesting. Which means they should have many faces, like we all do. A villain that is just pure evil is not a character.