The problem with your theory is that mulberry has the same basic characteristics as Osage, but it is still considered second string or alternative bow wood. If it were just characteristics, a lot of other woods (mulberry) would not have been overlooked. I think the concept of 1st string woods was created by people who had never even tried most of the woods we use today because they had a plethora of Osage and yew.
I've been wrong before Justin. Have you read any of the classical archery literature yet? It's very interesting and sheds a lot of light on discussions like these.
"Mulberry, Sassafras, bois d'arc, souther cedar, black locust, black walnut and slippery elm, are valuable woods, in the order named, for making bows..." Maurice Thompson,
The Witchery of Archery 1878
"Osage orange, mulberry, locust, black walnut with the sap wood, red cedar, juniper, tan oak, apple wood, ash, eucalyptus, lancewood, washaba, palma brava, elm, birch, and bamboo are among the many woods from which bows have been made." Saxton Pope,
Hunting with the Bow and Arrow J. D.