Another Fence Post Proposal
The problem with Senator Markey's proposal isn't that it's a violation of anybody's rights; the problem is that provides a foundation for future violation of rights. It's another fence-post proposal, earlier discussed here, here, here, here, and the original inspiration for this metaphor here. In the absence of such a bureaucracy, censorship is unlikely to be effective and its ineffectiveness might act as a discouragement. In the presence of such a bureaucracy, we're one constitutional amendment away from a tyranny.