I've tried wood (and metal, cardboard, various plastics, hard rubber, and other stuff). I made a pick from basswood that had a nice mellow tone, but it didn't last very long. Crow's speculation is right, roundwounds chew up soft wood, and the nicks/chips/splinters that result give you an uncontrolled sound (and inhibit your picking motion).
I suppose you could make a pick from a hardwood like mahogany, or maybe even ironwood, that would be durable enough to work with. But it sure strikes me as a labor intensive process to shape and polish - plus it's hard to work small pieces of wood precisely, as there's not much surface for a clamp or vice to hold your work - and even less room for your tools.
The basswood one I did years ago I did by splitting a small block along the grain with a chisel, cutting out the basic shape with a coping saw, and then doing edge shaping with a pocket knife. It was probably 4-5mm thick when finished, and felt pretty good. If I'd used a harder wood, I probably would have tried a small vise with a Dreml tool to shape the edges. But then I would have had to make my blank with a table saw or something, because hardwoods don't tend to split nearly as cleanly as softwoods.
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