I assume that the possibility of a beak growing too much from not been used exists but I've had parrots that I've never seen chew anything and their beaks were just fine. As a matter of fact, I can count with the fingers of one hand and have some leftover the times I've seen Isis Redbelly chewing anything and, when she does, it's always soft (cardboard) and her beak is perfect. Passerines' beaks grow at a rate of a complete 'turn' (meaning from the bone to the tip of the beak) of two years and even though they NEVER chew anything, they don't get overgrown beaks unless they have liver issues.
Thanks for the answer, Seagoatdeb. It is true that years ago nobody knew much about birds and their health issues. I took my first rescue (Pretty Bird, a RLA) to the only hospital in Manhattan that treated exotics back in those days three times, all three times I got a different vet and all three times they told me that her crooked legs were, most likely, a birth defect or caused by a metabolic imbalance when the poor birds had broken bones in them! They never even thought of taking an XRay and stupid me never thought of asking for one, either!