To go back to the original question: I think it would be better to teach your children how to filter the internet for themselves. There is nothing inherently wrong with the internet – it is merely a “place to put information.” Teaching your children right from wrong is a big part of chinuch – you cannot always just cut your children off from the outside world.
For example, you teach your children how to keep kosher. Aside from not mixing milk and meat, in your kosher home, what do they have to worry about eating kosher? Nothing! Because all the products are kosher. But still, you make sure they understand what makes things kosher to ensure that when they leave their home, they can still eat properly.
If you teach your kids how to use the internet for kosher things, then they can learn to stand on their own two feet. That does NOT mean you should leave them unsupervised, but it means you should help them with support.
By the time they are adults, the world will be even more dependant on the internet and virutally all jobs will require computer/internet knowledge (for the most part they already do). You are not doing them a favor by shutting them out.