Your first part is precisely why I sometimes let kids keep toys at their desks when doing work with them. I make it clear, "As long as you answer the questions/do your work, I don't mind if you keep the toy." Sometimes a stim toy makes the difference. As long as it's not distracting them away from what we've got to do, it's fine by me.

Besides, when I went to training for my current workplace, we were encouraged to bring our own stim toys. I used a spinner pretty much the entire time. Another coworker brought a bag of various squishies and pop-it toys to share as well. If it's acknowledged as useful for us as adults, it should be acknowledged as useful for the kids.