When I attended various sessions at NAEYC, the stick issue would come up. (see my notes)
For such a simple open-ended toy, there are a lot of concerns that come up if you try to include it around kids.
“What if a kid swings it around or runs with a sharp stick and gets hurt?”
Totally legitimate concern. I asked Ellen from the Outdoor Classroom about this after the workshop and she told me that they don’t have an issue with this at their school. Apparently, this is due to the way items are introduced at the school, as well as the culture with the kids.
Regarding the desire to swing a stick around, one participant at a workshop said she gives the kids such an option. However, she lets only  one child do this at a time, at a space far from the other kids. She said that usually the kid would get bored and come back to the group.
I can see both sides of the argument- On one side you have the concern of safety, and on the other you have the benefits of using a great, simple, loose part. There’s even a book on all the things a stick can be! Also a stick is on the toy hall of fame.
Of course, there is also a fear of safety liability or lawsuits. Ultimately, any risk should be put through a risk and benefit assessment. Then each school can define their own culture.
Related to this is the conversation about it being used as a pretend weapon. That is a whole other issue.
Providing large movement items where the kids can use their strength to show off their power.
IT also makes me think of the quote from Mister Rogers in the November 1998 Esquire article (recently reprinted in April 2017)
Oh, I just knew that whenever you see a little boy carrying something like that [a sword], it means that he wants to show people that he’s strong on the outside. I just wanted to let him know that he was strong on the inside, too. And so that’s what I told him. I said, ‘Do you know that you’re strong on the inside, too?’ Maybe it was something he needed to hear.