An interesting discussion - I suppose if war materials and labour were an issue, then potentially the wooden scabbard has some drawbacks. After all, it is more labour intensive and cannot be simply cast like a metal saya can.
I would have thought that metal sayas provided better protection particularly from crushing forces than wooden/lacquered scabbards due to the tensile strength of metal. This would be particularly relevant when soldiers had an expensive, historic or ancestral blade mounted. The Rinji katana that I possess, has a high-quality blade but is mounted in a lacquer saya. Sure it is lighter, but metal does provide better protection when you have gone to all of this trouble to purchase an expensive blade. I am aware that Rinji swords rarely have metal sayas, but that is beside my point.
Furthermore, theoretically a painted metal saya somewhat negated the requirement for a leather combat cover, requiring less protection from moisture than a wooden saya. I am also aware that a lot of troops carried metal sayas inside leather coverings.
Food for thought,
Andrew