I was not a fan of suckers. I was even less of a fan of suckers on hard sticks. And especially opposed to them when they were passed out to kids by men dressed as giant bunnies on playgrounds. I didn't have a problem with the man in the bunny suit. It was the idea that he was passing out suckers on a playground. SUCKERS ON A PLAYGROUND!
Growing up, I was taught that suckers were a choking hazard. I was only allowed to eat them while sitting still. If I ran with them, they were taken away. My mother was so afraid I would trip and shove the sucker stick so far down my throat that I would end up in the hospital for days, if not dead from choking on the candy part itself. It was rare, but it could happen.
If there was even the remote possibility that a child could fall and get injured by something you gave them, would you still give it to them? I wouldn't. And if I did, I would watch them very closely to reduce the risk of the situation. That's called close "adult supervision". That isn't something you always get at a playground. I surely wouldn't give my kids a sharp pencil, a knife or scissors and tell them to have fun at the playground. Maybe someone will put a little more thought into this for next year. There must be some sort of gift they can find that won't be a choking hazard or a dangerous allergen or candy. Might I suggest a sticker? Or a stamp on their hand would work and be more forgiving to the environment.
Moral of the story: As a parent, you constantly need to think about your children's safety. They might not like the outcome, but it could save you a trip to the emergency room and that should be worth it.