Omnipresent content moderation is never the immediate goal even if it's on the wishlist. Censorship is about targeting a group enough to negate their momentum, sometimes it's rebellious citizens (China), sometimes it's child predators (everywhere), and sometimes it's metrics that conveniently correlate with the opposition (hatespeech against Republicans, transphobia against black comedians, family values against Democrats). The irony is that you can't even count on past beneficiaries of censorship protections (LGBT community, African Americans, the silicon socielities post-crypto wars, assorted denominations of Christianity, the ACLU, etc.) to protect them. After people win in the arenas that matter to their cause the ladder stops being valuable and it becomes more useful to silence critics who might slow you down.
Edit: Oh yeah, and the press who quit caring about championing speech rights when the internet started killing them.