Yikes....little stinker!! That's when the video monitor comes in handy too!
I have one 3 year old who sometimes wears a necklace. It usually comes off before lunch (her own choice) but if not, I make sure to take it off before nap. I've also had to start taking her ponytail out because she has a habit of putting it on her wrist or ankle and I don't like that. She also has her ears pierced and those could fall off too I guess? Heck, even my own nose ring has fallen out and it took me months to find it!!! Lol
I view necklaces in the same category as scarves, shoelaces, string on clothing and dress up clothing, ponytails, play masks etc. I don't outright ban them but make sure to use caution. It's kinda like the swing issue too right? Some don't have swings on their play structures and some do. IMO, it's good for kids to learn how to be safe with certain things.