Raise bullies? You are putting a whole lot of faith into the idea that parenting alone shapes a child's behaviour. And all kids are different so your burden isn't even amongst the population. The level of involvement for one kid might be near zero while another requires near constant attention. Are you okay with putting additional burden on parents based on the needs of their particular children? Are you prepared to define what "responsible parent" actually means in a concrete way that everyone can discuss, or can I just say yes I pay attention and I spend time with them therefore I am a responsible parent?

What kind of punishment are you talking about? If you imprison them what will you do with the kids? If they are poor and you fine them, is that going to be a net win for society?

And teachers? Teachers these days have near zero enforcement options. You can't make them responsible unless you also give them back some power. They sometimes suffer abuse from students as well.