I'm hugely critical of our industrial-age schooling system. But I think it's a mistake to suggest that bullying is only a factor in those schools. Bullying happens in families, in churches, in neighborhoods, in workplaces, in any environment where you have groups of people. Primates are big on dominance hierarchies, often violently enforced, and humans are definitely primates.
Everybody needs to learn how to deal with bullying. How to recognize it, how to combat it, how to build relationships and cultures that are proof against it. And if there are things we want everybody to learn, school doesn't seem like a bad place to start.