Having been a kid who benefited heavily from access to networks (pre-Internet and Internet), and who went to college while still a "kid": no, absolutely not.

Kids are, in fact, humans, and should not be disadvantaged because of their age.

I've seen plenty of stories on HN and elsewhere about particularly clever 10 year olds who found their ability to participate online destroyed because some service provider figured out they're 10 and COPPA came into play.

Depends on if you want them to be totally unprepared for society or not.

Would you consider it reasonable to ban anyone under 18 from reading or visiting a library?

Even though children do have fewer protections from the 1st Amendment, they still are covered by the 1st Amendment in the US. I think it's very likely that a federal ban on children accessing the Internet would not survive 1st Amendment muster.

There are things we can restrict children from accessing and talking about, but it's a lot more narrow than people often suppose and most of that restriction is usually coming from private actors (particularly parents) who aren't bound by the 1st Amendment. Outside of settings like school, the government is generally not as free to impose those restrictions.