>What I want to say - you just beating up a bully will mean some other kid(s) will get beaten up (or beaten up even more) further down the line.

I can tell you first hand this definitely isn't true in all cases.

We had a bully at my school who constantly picked on all sorts of people. Eventually he decided to pick on one of my best friends who got sick of it and took him to the ground and punched him in the face about 15 times.

It was like a light switch - the bully became one of the chillest, nicest kids in our grade after that. He figured out pretty quickly that getting punched in the face isn't much fun and decided it was probably better to stop being a dick to everyone around him because he didn't know who the next person was that would return his shenanigans with violence.