Generally the shield isn't just wood though. A layer of thick rawhide can add a pretty surprising amount of protection.

I don't really buy into the "missiles got too powerful" theory, partly because I doubt that the kind of power produced by a powerful crossbow or longbow would be something completely unheard of, even during the dark ages. A hefty spear, for example, thrown by strong individual might achieve up to 200-300 joules of KE. And vikings really did love throwing spears.