Neither of mine ever used a binky. My firstborn started biting the nipples off his bottles at 14 mos when he got all 4 of his front teeth at the same time, so the bottles had to go.
I told him when you can eat your bottles, you're too big for them. I had him round them all up and throw them in the trash, then we went shopping for sippy cups - ones with cars on them. He thought they were TOO cool!
With dd is was tougher to get rid of the bottles. She'd get sick and *need* her baba. We went with the weaning off approach and she was over bottles by 2.5.
Oddly, the grandbaby got her own self off binkies. She hid them all like pirate treasure and we still don't know where they are!
She ditched the bottle as soon as there was a sippy cup in the house and never looked back (she was about 1.5).
I say, like potty training, they let you know when they're ready. Apples fall off the tree when they're ripe.