You literately wrote “If there is one person that has all the influence, it’s you as a parent.”
Yes, because it's true. The kid spends most of it's time in your care. But that doesn't mean you can negate all the other influence. But you can and should keep track of what is happening in your childs life.
but now you shit on people that for one or another reason have children that turn out badly
I'm not really trying to shit on people, sorry if you get that impression. There are reasons why children turn out bad despite you doing your best - especially if the partner leaves and you're a single parent. It's nearly impossible to feed yourself and your child while still paying 100% attention to what it does.
However, my impression is that many people want to have children but not take care of them. That's what I see in my daily life. Kids come home from school, get something to eat and then the parents put them in front of a TV or a tablet so they can keep themselves busy while the parents do whatever. And don't get me wrong, it's not even wrong to do that every now and then. Everyone needs a pause. But in many - especially poorer - families, this is common practice and it's no surprise the kids turn out as they do.
Do you think that it is the parents full responsibility, that their 13 year old child committed suicide because of bulling?
If bullying gets to a point where it's so bad the bullied kid feels the need to kill itself, there's so many things wrong before that. It's not like a child is bullied once and immediately jumps off a building, that is a long process that goes on for weeks or months and the changes that happen to the child are noticeable to adults in the childs life. Doesn't want to go to school anymore, scared to go out etc. - if you're a somewhat attentive parent, those change are noticeable. My mum, for example, almost always ate lunch with me when I came home and talked with me about the day. If I was bullied, she would've noticed within days.
So no, they don't carry the full responsibility. But they are certainly partly responsible, even tho that might sound cruel to you.