From my personal experience - my parents didn't try to limit or control my online behavior and usage of a computer at all normally, which got me into few weird situations but also allowed me to learn how to recognize and deal with them. When they tried restrictions as a punishment, they never succeeded in any way. At one point when I was around 12-13 years old I simply bought an older laptop they didn't know about.
Today's smartphones are much cheaper, more powerful and widely available - practically every older classmate has one in a drawer somewhere and will happily sell for a few bucks. Let kids learn how to behave online while unattended, because they will be online unattended.