From Erik Lauer:

Liliana of the Veil is a very efficient planeswalker, maybe the second most constructed after only Jace, the Mind Sculptor. Black was underpowered after Scars of Mirrodin block, and she was part of what brought the color back into balance. When we tried her again, it was less about any particular synergy, and more about her incredible impact for a 3 mana card.

From Ian Duke:

I was a tournament player during the original printing of Liliana of the Veil. She was certainly very powerful in standard then as well! Like Erik mentioned, I suspect the reason she ended up as strong as she did was because black was weak in Standard at that time. We generally try to avoid putting so much of a color’s power into a single card, so as to create more diversity in deckbuilding. When we tried Liliana again in Magic 2015 (with the simple goal of being an exciting reprint), we were just coming out of an era where monoblack devotion was very strong. It was clear to us in playtesting that she would not have been healthy to add to that format. And yes, she was causing problems to the point where we tried anti-discard text on some cards to counterbalance her.