We used to put a tax on ships arriving from Italy and other places... they must bring Yew staves with them to dock in our ports or similar, i'm going from memory. Our Yew was more stunted, twisted and knotty, while theirs was straighter... warmer climates, trees grew better... Far more suitable for bow material. I seem to recall the Amesbury Archer had a Yew bow, but it was of poor quality comparatively. Yew bows in the Neolithic/Palaeolithic etc were used for hunting larger game. Aurochs, Red deer etc, and not many could use them. It wasn't until much later did they become the first choice for a war bow. Even then... it took a lifetime to train an Archer to such a bow.Very few have been found but that is not proof of not being used. Willow bows have been reproduced that are very capable of taking out wildfowl. Yes, it's a poor material but in the early Mesolithic will have been one of the only materials available.
But, you are picking up on just one material of my more generalist statement - there are many woods used for extensive periods before yew and even when yew was available woods like ash and elm were still used very frequently - there just wasn't enough good yew available especially at the time of the Mary Rose. I can't remember the ratio but was it 9 ash bows to 1 yew?
So i guess we we don't have a traditional bow material then? Yew is the obvious one folk will pick, as its what most folk know...and what history records as such.