I see two problems - first of all, beginners are unlikely to know about this method of wish-saving. Second of all, it erases all of the sense of "luckiness" at getting a wish, by letting you keep it in reserve for as long as you want even if it's from a pool, or something like that.
Other than that, it's mostly a well-understood rule of wishes that you can't wish for more wishes, and that includes wishing for another chance to make a single wish.
A far better idea would be to simple provide a method of saving when the wish prompt comes up, perhaps with an extra protection that forces a "restore" when next running the game and stopping people from saving a wish-prompt indefinitely and backing up those saves in such a state without extensive knowledge of how to bypass it. Obviously, there will always be ways around it, but then, the idea here is to maintain integrity for most people.