Why play "assassins" instead of Annie?

I legit don't understand why anyone would pick something like Diana, Zed and Akali when there's Annie. Ok, I understand Annie has only Flash and Protobelt as a gapcloser but she also has a stun, range, more AoE, much more tankiness with W and a far safer laning phase than assassins. Annie's natural range is basically as much as the distance of an assassin with a gapcloser. So why would I want to use Diana R to gapclose when I can just pick Annie and have basically the same range naturally without using an ability.

I know I'm oversimplifying but I just never really see a point to these assassins when Annie exists. She seems like a better version in almost all cases.