They invented it precisely because they didn't have access to forests.

Drawing a bow places very different forces on the inner and outer faces of the bow. The outside needs to be strong under tension, but the inner face needs to be strong under compression, and both need to resist that force. There are a lot of materials that are great at one or the other, or ok at both. The Mongolians, lacking access to forests, were forced to find a way to get both using materials at hand, developed the composite bow. By laminating various materials together they were able to get all the necessary strengths in the right places, and mitigate the supply issues. Additionally, since using a longbow almost the size of your body on horseback is a good way to be a terrible and very dead horse Archer, the mongol was heavily recurved. Placing a recurve of that degree in a single stave bow is practically impossible, but is a simply a matter of adjusting your glue form with a laminate bow.

The English, however, had plentiful access to the yew tree. Yew is a wonderful wood for a bowyer. The heart is extremely strong in compression and can take a lot of force withoit splintering,(ideal belly wood) and the sap wood is very strong under tension, making it a perfect backing wood. Why fuss around with a much more delicate laminate made with medieval glue, when the perfect one has grown naturally in the forest. The longer bow size wasnt an issue since the English weren't mounted, and the straigt single stave construction was much more rugged. English long before also weren't flat, the belly has a D shape. This lets you load the bow with immense forces, but isnt something you can do with many other bow woods.

Tl/Dr. K.I.S.S and Necessity is the mother of invention .

Source . Personal study and experience. If this comment isnt wholly accurate or properly sourced, I heartily apologize and will promptly delete.