I don't expect the English particularly cared where the staves came from as long as they came, and I think others have suggested in the past that they were using high altitude, hard to get yew at the time of the Mary Rose because all the easier to harvest ancient growth across Europe had been cut down already and yew works on about a 80-100 year coppice cycle. If you were trying to make money selling wine to England and one of your business overheads was to provide 10 yew staves per barrel then you would presumably shove whatever yew staves cost you the least into the ship. If medieval civil servants had the same job satisfaction back then that they do today I can't imagine they would be inspecting every yew stave passing through their hands for suitablility as a bow, but they would just count them and leave the details to the bowyers. Maybe that's why the levy got increased from time to time - quality of staves was reducing so the pool needed to be bigger?
Even today coniferous forests that are grown exclusively to cut, ie effectively a crop in a field, grow for about 50 years in the case of Sitka spruce and 80 odd years for ash just for a couple of examples, so multi-generational forest management is still entirely normal. It's only in the last 100 years or so that ancient pollards stopped being routinely cut, which is why our woodlands are now in such bad shape.
