I have definitely seen benefit's in seasoned wood (even white woods like oak and yellow woods) but am curious as to why and how a large piece of wood such as a stave would get much harder and denser while a selfbow made out of unseasoned wood might see little to no change over the years. The wood that has been turned into a bow would technically still be seasoning.
I made a bow out of Sumac about 1 year ago that was seasoned (or dried) within 3 month's of harvesting it and I checked the weight on it a week ago and it's the same draw weight as it was when I built it 3 month's after harvesting.
And while darker wood's such as Osage will have more compounds and oil's in them naturally, even white wood's and yellow wood's have compound's in them that should harden over time as well since that is a part of what gives them durability, weather resistance, and so on.
Perhaps the wood has to season by letting it dry out extremely slowly without ever reducing it down until year's have gone by?