Hmm...this is kinda tough. I think there is an age where you're just too young to really know what you might want later in life. For example, I actually do have bipolar disorder and when I was 20 I thought there was no way in hell I was ever going to have a kid and want to pass that down. However, I got to be around my friend's kid and that changed my mind. I had my son when I was 24 and I wouldn't change my decision for anything. If you would have let me, I would have gotten my tubes tied at 20 and never have had the chance to have him.
I'm not sure what age is "too young," but I do think early 20's is probably a bit early to say for sure that you won't ever change your mind and do something permanent. There's always birth control in the meantime.
On the other hand, I don't much care for being told what I can and can't do by doctors or the government. So I don't like the idea of being told "you must be this age to do what you want" either.