My son... was about 3 when we took his away.
He was a CONSTANT binky user... all day and night.
We told him, that Santa needed it to help the other kids.... and he's a big boy. Then, with him, we collected ALL the binkies in the house, put it in a bag.... and sent it away. (we actually stuffed it in a closet). And that was that. We EXPLAINED to him in a loving way... that Santa needs it... and he is helping Santa. My son understood...
It took him 2 days to adjust without it. He also had a lovey, though, that he slept with.
My son, after about 2 days, slept fine, he didn't tantrum about it... and that was that. I was astonished that he adjusted so well... being that he was a CONSTANT binky user.
Christmas is coming up... maybe try that with your kids? Tell them, Santa needs it... etc.
We had to take away our son's Binky, because his mouth structure was being affected... and his mouth/teeth, was malforming. It took about 6 months to 1 year... for his mouth to go back to a normal formation.
This can happen with constant binky use, to some kids.
all the best,
Susan