> it will only make the bullies taking their revenge on vulnerable ones with even more cruelty. And they will plan it carefully to be hard/impossible to prove. It will lead to the escalation, not to the resolution

Bullies are generally not very intelligent. Deterrents absolutely do work if applied consistently. A society that applies corporal punishment at multiple levels, as Singapore does, strongly ingrains the idea to straighten yourself out, because there's always someone with a bigger stick.

> In severe cases, I can think of suspension or exclusion from school or another kind of isolation.

In my experience, this isn't the deterrent you think it is.

Bullies certainly can be intelligent. Intelligence and sadism are orthogonal traits.

The only thing that unites bullies is the willingness to inflict misery on others. A bully could be a simple thug who uses violence because they have nothing else going for them, or a popular kid at the top of their class who manipulates others for their own amusement.