but a willow shield needs to be made and a soldier will always have clothes with him.
Also slingers weren't traditionally warriors, but shepherds - or at least from a shepherding tradition. A fleece wrapped tight would actually work quite well against a blunt (most were) sword or a knife.
Raw fleeces would be fairly cheap and easy to get hold of (for a shepherd).
Could possibly by the origination of the practice.
But from a practical point of view it would certainly make reloading tricky - particularly if he's got his ammo pouch on the wrong - ie: left - side.
Again I think artistic licence has well and truly been abused there