Surveillance has a chilling effect, even if you're not doing anything wrong. For the same reason I wouldn't develop the same socially if my parents had forced me to wear a wire in the school cafeteria, I wouldn't be nearly as freely curious if my parents were watching and questioning my web browsing. I'd probably have become an entirely different person.
Personally I think parents should look out for Very Bad Things like sharing phone numbers and addresses or meeting with strangers, children living on /b/, people advocating real-world violence, etc. but if the internet is a family-only activity, children will never learn to use it to its full potential.
Time limits on the order of a couple hours are pretty reasonable, but I'm talking about people who set a limit of 15 minutes/day, or wealthy families that deliberately have one computer shared with 6+ people because they don't want it to become significant in anyone's life.
Also you are probably not going to become a programmer if your parents are nontechnical and installing software on the shared computer requires extensive justification/begging that usually leads to "no."
I could just be biased by the kids I knew, however. Their parents saw the internet primarily as a strange and foreign threat to be mitigated, and so all internet activity was bad until justified by "legitimate" need, rather than encouraged unless dangerous.