Why is Vayne so popular?

I'm a support main. It feels like every other game I end up paired with a Vayne player. While Vayne has a terrifying late game, I really dislike laning with her because of her weak early game damage and susceptibility to being shut down early. It takes a lot of skill to play well as a Vayne until you can get a few items. Meanwhile there are a number of safer and/or stronger carries in the current meta. Personally, I enjoy (and feel it fits my playstyle better) when I get a high burst lane partner who's strong in either the early or mid game.

So why is Vayne still picked so often, when you could be picking a Corki, Ezreal, Ashe, or Jinx?