(devil's advocate) Your analogy is bad because "rounding up" is something one Does Not Do Without Due Process, whereas deleting an intertube site is not. (America managed for 200 years without any intertubes at all, you know, so it can't be all that important.)
A closer analogy is shutting down a printing press. America survived for 100 years before offset printing existed, so why not craft a law that excludes newspapers that use offset printing presses from first amendment protections?
The hyperbole around this law is getting irritating. Congress can't restrict First Amendment rights online any more easily than they can in print; laws cannot override the Constitution.
The constitution and other agreements on human/civil rights are frequently violated by the American government. Why do you expect this case to be any different?
The problem is the gray area in between. Once passed, the law is the lay of the land. Its constitutionality can only be challenged once you've been charged with it. In the meanwhile, your livelihood is offline.
It's not uncommon for a law to be passed that is unconstitutional.
Just because the government sometimes gets away with unconstitutional things, it doesn't follow that there is no check whatsoever on the government's power.
For example, the government might get away with indefinitely detaining a few people without trial; but they might still forbear to arbitrarily detain more than a few percent of the populace for fear of popular revolt.
The constitution is just a piece of paper. It only has force so long as people allow it to. And local and federal laws can violate the constitution up until they are overturned by the courts (potentially a lengthy process).
It took nearly a century for the 14th Amendment to achieve the full force of law everywhere in the US.
We should not be the least bit blase about allowing unconstitutional laws to be passed, as though they would be null and void upon passing.
