Many decades ago when I was still young, I was bullied and reported it to the authorities, but they didn't care beyond giving the usual empty "be nice and get along" verbiage. Ended up fighting the bully and gave him a few deep bleeding cuts with my nails. I got in trouble for it, but he never dared to touch me again.

That’s generally the solution for bullies. I wonder whether that is also the solution for victims, making them strong enough.

There's no denying a broken nose and some lost teeth will make many bullies twice about trying again.

Problem is it's often illegal or against the rules to do it since deliberately beating the crap out of a bully isn't self defence in the traditional sense. And in the cases where it doesn't work, the situation may escalate or the victim might end up being punished harder than the bully.