Yes, the parents should take responsibility and make their own children reponsible.
No, kids should learn to be responsible the hard way.
There is no universal answer on how to raise a child-- every child is different needs a unique system of negative and positive repercussions of their actions along with the ability to make their own decisions, whether you as a parent believe they are bad or good and let them make their own mistakes. My general opinion is that parents need to take responsibility for doing things like teaching their children right vs wrong and let the child make their decisions from there. Telling a kid 'do whatever' is bad parenting and giving them room to make their own decisions despite your opinion and being there if it goes wrong, is good parenting. A responsible parent doesn't mean a controlling parenting, it means a parent that sets helps and loves their child.