Same here.. But, at 16 months old, Ari Does this much less then he used to. It's now an exception rather then the rule. When he goes after a stick - I don't try to wrestle it from him, it's his now and his protective of his stick, so I try to lure him away.. Get him to chase me, for example.
But I also noticed this. We often go to nature parks for walk - trails, trees, lots of sticks to eat.. And we also go to the woods behind the back yard - a quick toilet trip early morning or late evening. So, when on the trail in a park - he never goes after sticks. Totally consumed by chasing different scents around. But he does that sometimes in the woods behind the backyard... Which leads me to think that when he tries to eat a stick - it's out of boredom, more then anything else....