It's complicated, as someone who was bullied in school, it hurts. It leaves wounds that two decades later I am still dealing with. But, at the same time, bullying is generally because the person is lashing out in response to their own shitty circumstances and children are the least equipt to analyze their own behavior.
Generally, but not always - you can't get too caught up in the idea that bullying is a symptom of the bully's circumstances, there are too many cases where it's basically a manifestation of sociopathic/psychopathic tendencies.
So, that being said children who bully others need to face consequences for their actions, but they need, more than that, to be given a better support system for dealing with their issues. And more than the bully being punished, the kid being bullied needs support and care to help heal those wounds.
We need a system that turns bullies and the bullied into stronger, kinder, healthier people, not into criminal and victim.
First the victim needs support, proper support that includes addressing the reasons they were vulnerable to bullying in the first place.
After that the bully's needs should be addressed, but with great care taken that their victims aren't used as a tool to try and "correct" the bully - too often victims get used, with an attempt to leverage their trauma to try and fix the person who traumatised them.
Coming down
hard on bullying is a necessary precondition for everything else, though.
I meant academic record though. Not a criminal record. With good behavior it should get removed. I could see how that idea is still too extreme because of what you said.
A system that addresses bullying promptly and thoroughly shouldn't require that kind of thing, even in a fairly moderate form. If bullying is addressed promptly and effectively then bullies just won't bother, at least not at or around school - bullies bully for
reasons, which generally boil down to some form of gratification at having power; take that away and they'll either address their desire for gratification some other way, or they'll grow up and get over themselves.
But realistically that's probably a pipe dream - dealing with bully promptly and effectively is really hard and it takes lots of resources, careful thought, and understanding, all of which are in short supply in most of the contexts where bullying is a major issue.