You pretty much have to whitelist. I think we're heading towards a future where we give kids only devices that restrict internet access to known good content. There's more than enough known good content out there already to keep kids occupied until they come of age.
There will be managed whitelists that your kids can access, which sites must apply for and demonstrate compliance with the policy of, and you will be able to trust, so that you or other guardians in your family don't have to manage the minutia, which is effectively impossible for you to handle.
And your children will be able to access only these, and any other exception that you personally whitelist them to have.
And we other adults won't let kids, yours or anyone else's, have open access through us as proxies, just as we won't buy them cigarettes or alcohol if they asked us, because we all agree doing so is wrong. And we will have punishments for those who break this rule, just like we have had for generations for pre-internet vices.
We won't need to bother trying to censor the whole internet anymore. We'll just take away children's unlimited unsupervised access to it, just as we have come to a social and legal consensus to exclude them from other parts of the physical world we all agree they are not ready to handle.
I predict this will happen, major device makers like Apple will lead it, and everyone will eventually agree it is appropriate and in best interests of everyone.