The very biggest Shiitakes I have grown were on bags of...mostly sawdust/turnings from a friend's small commercial woodshop specializing in Myrtlewood items. I tried some additives, too. So, I suppose the small window for use of fresh wood is because the wood will pick up competitors...other fungi, mostly. When we buy mycelium it is typically on sawdust or dowel plugs, so it isn't the age per se of the wood that is the issue. I had one unit that was 1/2 lb.
So, Naeem, this is a different aspect of your question. Trees that were cut and left out to get contaminated would not be good candidates. Wood that was not very contaminated and can be sterilized (I used a 'turkey" oven bag) can be used; in fact, it is common in commercial applications.