... or only grant patents if the inventor has a fully functional prototype of their idea.
In principle, a patent is supposed to cover this. The text of the patent has to provide a recipe for reducing the idea to practice. As I understand it, if the recipe is unworkable, the patent is void.
Whether the patent office is stringent enough about this requirement is an open question of course. It may vary from one field to another. For instance, a patent for a new kind of optical lens is required to include a complete "prescription" for the lens, which is recognized as a sufficient set of data needed to replicate the idea. (One of my patents is like that).