Wood is a very inert material, easy to shape into shapes suitable for stirring. It is less aggressive to food than metal , for example, which can scratch the container. It is true that, in the case of paella, it would be a culinary sacrilege to stir it after adding the rice, although you do have to do it first with the stumbling blocks and the base broth. According to popular knowledge, non-stick and stainless steel paellas are also prohibited, perhaps because the rice reacts with the iron in the traditional paella, which transmits some molecules that give it a certain iron flavor.
The wooden spoon is also suitable for pastries , jams and purees, as it allows better binding of ingredients and achieves a pastiness that cannot be achieved with metal.
