Whitelisting is a better idea than blacklisting, certainly. And parents (usually) know better than most what their child should be allowed to see. But once again, ignorance is the child's enemy, especially if parents don't do their homework when working on a white list, either because they're too busy, or they have more faith in the software than it deserves due to its inherent limitations. For example, kid asks parent "Can you unblock HotKiddies.com for me?" Parent goes "Sure" and proceeds to whitelist it, not knowing that (in our scenario) HotKiddies.com is a child porn site. That's the risk when you put that kind of burden on busy parents, and if we're "thinking of the children," then we have to think of that.
This aside from the obvious point that if a kid is more technically knowledgeable than their parents, they'll have plenty of opportunities to hack the software and whitelist whatever they want.
And, of course, the question of what to do in schools and libraries.