They are a platform distributing UGC protected by the CDA. Any discussion of “common carrier” is entirely orthogonal, and basically nonsensical in the context

They are a platform distributing UGC protected by the CDA. Any discussion of “common carrier” is entirely orthogonal, and basically nonsensical in the context of something like Twitter. “Common carrier” generally arises as a trade-off for a government granted monopolies based on limited access right-of-ways. This was true for railways, and true for telephone wires. Why would this apply to a random service like Twitter?