Wishes can come true by itself or not. Maybe, it’s because human beings have many desires that it was made that way. It teaches us acceptance and perseverance in so many ways when having a wish.
But I’ve always believed that wishes come true either way. Sometimes, its just that we didn’t try hard enough or that it wasn’t meant for us. It doesn’t mean we should give up easily though, we may not get wishes granted the first time but it can always happen the second time we try. While you can’t grant your wish, maybe you can grant others wishes instead and be a genie – see here.