No, this is the end of the ad-supported internet.
Politics doesn't matter; the (US) government cannot legally censor anything, they've tried, it's been declared unconstitutional. Companies don't care what they're hosting, as long as they are getting rich. If they could legally make millions of dollars a year hosting child porn, they would. (They have no objection to polluting the environment or forcing workers to work in unsafe conditions, directly resulting in many deaths every day. Showing videos on the Internet is child's play compared to that.)
However, it's the advertisers who will get upset, and then pull out. "Our product associated with porn being shown to children? Bye." With no advertising revenue, the web (as we know it) cannot exist. That means either censorship (too hard; "information wants to be free"), or actually paying money for content.
FWIW, this is not unheard of. The big Japanese video sharing site, NicoNico Douga, requires everyone to pay. Even though it's not free, it's more popular than Youtube.
In the end, the advertisers lose, and I think that's a good thing. I hate advertising.
Media corporations have already started demanding more control over the "distribution channel" that is the Internet.
They're demanding, but nobody cares about their demands. I know people whine about Hulu's restrictions, but I've never even visited Hulu and I still get all my TV online. It's called Usenet. You open your news reader, browse to alt.binaries.multimedia.tv-shows, or whatever, and download away. In 10 minutes, I have whatever show I want, in HD, with no restrictions. "Censorship is considered damage, and the Internet routes around it."
The whole "let's punish file-sharers" thing has also backfired. Even governments with very weak personal protections (France, the UK) have struck down the disconnection laws. The Pirate Party has 17% of the vote in Sweeden (and large numbers in other EU countries, I think). Organizations in the US are suing the RIAA for its lawsuit intimidation campaign.
The tide is shifting, and it's not towards the media industry's interests.
Basically, now is not time for the media companies to demand anything. Nobody cares what they think. If creating content isn't profitable anymore, they should go into some other business and stop bothering everyone else.