Works for well-adjusted, rational adults (hopefully). Not so much for children. It's moral pornography.
The idea that public utilities (e.g. public broadcast spectrums) must conform to a negotiated standard of decency is well-established even at the court level. It wouldn't necessarily be protected free speech, even if the publically-accessible internet were a public utility (which it isn't), especially if private alternatives exist (which they do, e.g. tor).
This is why well adjusted rational adults are responsible for raising children. You teach a child what is right and what is wrong and then hope beyond all else that when they set out on their own you've given them a strong moral compass. You don't neglect the responsibility and blame the government for not censoring all the bad things on the internet from them when they screw up later in adulthood. Are you really arguing society should be 100% childproof? We can't put anything on the internet that someone might find objectionable to a child.
The idea that public utilities (e.g. public broadcast spectrums) must conform to a negotiated standard of decency is well-established even at the court level. It wouldn't necessarily be protected free speech, even if the publically-accessible internet were a public utility (which it isn't), especially if private alternatives exist (which they do, e.g. tor).