I will let them chew a stick at rest....and under supervision...(as long as i can see them) after all we have not got eyes in the back of are heads...
I wouldn't even allow this. Sticks can easily splinter and I have known where a dog has chewed a stick, got a splinter stuck in its mouth and developed an abscess as a result.

Unless you're worried that the sticks are from a poisonous plant, there's really no harm. Dogs love natural organic any thing
. Some dogs chew on rocks, some eat dirt, it just happens....
Right, I'm confused. I've stopped throwing sticks in the woods for Alfie because, although he actually waits all by himself after the stick is thrown so he can see the trajectory and move straight to it (IYSWIM) so I don't worry about that, he does often sit down with stick when he's starting to tire and gives it a good chew. I was worrying about sticks because of him swallowing splinters. Are you saying this isn't something to worry about?
It's costing me a fortune in substitute tennis balls though, even though I buy the good but cheap used ones off of Ebay, because we usually lose several a week. Although we're at the point where we've lost so many in the woods (not because he can't find them but because he puts them down when sidetracked and forgets where he's put them) that he's started finding almost as many as he loses.