I totally agree with this. Where I grew up, corporal punishment was legal for most of my schooling and frankly I find it absolutely abhorrent. Why an adult would find it necessary and justifiable to use a weapon on a child who has been naughty is something I simply can't get my head around, and absolutely condemn. Furthermore, violence simply teaches a child to anticipate a painful consequence, it doesn't teach them why what they've done is wrong. My parents used to hit me when I was a young kid, and I never really learned any valuable lessons from it, I just ended up with a lot of bitter and hurtful memories.
It's absolutely possible to discipline a child without physical violence.
To answer the question of the thread itself, I'd say yes and no. Yes, a parent has a responsibility to raise their child properly, but on the other hand, no parent has, or should be expected to have, 100% control over their kid 100% of the time. That's just not realistic.
Having said that, I've always found it a tad absurd that we need to obtain licenses for things like driving a car or owning a dog, yet having sprogs is a free for all. There are so many people who really, really shouldn't have children.