In the final analysis, the only one who can judge the amount of freedom your child can safely be allowed is you. I worry about explaining the dangers I see on the Internet. Their child will either go next door and access it there without any control or they will grow up crippled. Computers and the Internet are the beginning of the world they will live in. If they grow up without being at home in that world, then they will grow up without access to the skills, information, and ideas they will need.
People learn best while their minds are young.
By all means, let them play on the Internet. The entertainment there is unprecedented, the educational and informational resources mind boggling. Just don't let them play there without supervision. Be aware of what they are doing. If you don't have time to make sure that your child has responsible adult supervision, then you don't have time to be a parent.