Fiberglass also has high tensile modulus so it doesn't stretch much. A fiber with lot of stretch will allow the stress to break the underlying wood since it does not support the strips across the grain.

Plywood is a reasonably green material as it doesn't need fiberglass or any other fiber for cross-grain strength and the laminations are bonded under high pressure so relatively little polyester resin is needed internally, compared with, say, cold-molding. There are natural polyesters; natural polyesters and a few synthetic ones are biodegradable but I don't know if these are available in plywood.

A thought: glass-epoxy composite may not be as bad as they are claimed to be environmentally, at least in theory: glass fibers are supposed to be bio-soluble and UV breaks down epoxy, but I prefer to avoid glass and minimize epoxy . . .