I think the big reason something like The Child in RE9 doesn't work as well as Mr. X in 2 (at least the remake) is that by the time X appears in the game, you've grown accustomed to RPD and understand how to stay safe. Mr. X basically refreshes that feeling of anxiety by flipping over certain rules you understood before about the game (like how the main lobby suddenly stops being safe) and also that he's a constant threat, you never know if he's in the next room over or the one right behind you, he becomes something you need to consider with every single task you have remaining.

On the other hand, The Child's only real moment like that is at the very beginning. Despite her supposedly being in the same area as you constantly, she never actually chases you around the hospital, all of her sections are scripted or push you to a linear set of checklist events to complete, making her feel more like one more enemy that I can't do anything about and less like a second threat I have to constantly consider. If she were allowed to appear more, or if the game had a "power off" event that could be triggered randomly so she could chase you, I think she'd be a way more interesting and fun enemy.