Sometimes when you run off, squeaking in celebration, with the stolen idea slung over your shoulder, you've brought your world-building with it. And since character is plot, you may have brought both of them as well -- or at least limiting constraints on either.
The filing-off-serial-number process can do something to alleviate that -- sometimes. Switching genres or locations may also help -- but it may also make it impossible.
Even if you can switch the genres, you may have to lug along other attributes. Take a story where, during a rout, a son leads his troops to rescue his father, cut off by the enemy forces. There is a certain amount of social status imputed in that action. Perhaps the troops can be filed off, and the son made a wizard who arrives with fireballs and lightning blasts, to deal with a flock of ice eagles, but perhaps not. Even if it can be done, it shows there was a deep commonality that couldn't get removed: the son had to have power to pull such a stunt off. Taking the notion of a rescue means taking the notion of ability for the rescuer with it.
Then, that it has consequences has, on the other side, something to start the world-building, or character development, or plotting with. Always nice not to have to imagine everything.