Entrusting our speech to multiple different corporate actors is always risky. Yet given how most of the internet is currently structured, our online expression largely depends on a set of private companies ranging from our direct Internet service providers and platforms, to upstream ISPs (sometimes...
Not sure about the US, but in the EU that process does exist: anyone can submit a claim against any domain, and if the “competent authority” which can be a judge or a law enforcement agency, so decides, they add it to a list of domains to be blocked at the ISP level… currently meaning at the ISP’s DNS resolver (use non-ISP DNS resolvers at your own risk), but technically they could request routing or deep packet inspection blocks through the same process.