There's no need for a love rival due to how the story operates. He's so absolutely dead set on loving her to begin with (and is pretty explicit with it, which is more than most other characters in similar situations) and she's not dumb enough to be oblivious to it, and in fact either ignores it or plays along with it for her detective hobby, leaving there no room for any other character to come around. If it was more focused on the romance, than it would make sense, but romance is only 45% of the story.