very cool concept! I feel like it adds a level of fun to the standard formula. It’d be cool if the offscreen ghosts/defeated ghosts could jump from object to object, with the spirit sometimes passing by the player’s screen as they transfer between objects. Then you could go ghost hunting! Also might be worth considering the implications if multiple ghosts end up on the same screen… for example it could spawn unique battle instances with more powerful ghosts.
When I think of great takes on the generic battle system Pokémon has to be up there. Not only do the game’s mechanics have you actively searching for random encounters in grass (whereas typically players groan and try to avoid such things) but they also have the trainers who’s facing direction is the trigger, allowing the player to potentially navigate around encounters they don’t particularly want. That kind of game design is genius because it makes busywork feel rewarding and under the player’s control.