There are cultural differences, which is why kids do sometimes switch schools.
IME (and it just mine, so take it with a grain of salt) kids who are experiencing issues like bullying don’t tend to move up the food chain, but rather laterally or down. I would imagine that’s because given a choice between two kids, one who’s been successful and happy in their current environment, and one who’s had a history of trauma, the former is a safer bet.