No leftists I know push for platform-provided censorship, because that inevitably harms left voices; eg: facebook taking down Crimethinc and It's Going Down: https://crimethinc.com/2020/08/19/on-facebook-banning-pages-...
(Writing this from the EU, where most of the people have watched the past US election season with... "amazement". Especially the way in which both sides seem to feel they are the oppressed side.)
It'll be interesting to see how EU/Western Europe copes over the next 20 years, if they cope at all.
Liberals are a dying breed.
ML's are probably the only ones who have any ideas of their own and support certain levels of freedoms at least.
That's a complete aversion to evidence.
To quote one in the USA.
"The right of the worker to have access to information is one of the most important of human rights. All information and technology should be held by the state whereas the state should proffer all information to all workers."
Well, we know how that works out. The person controlling the information is in control.
The difference you seem to be overlooking is that basically no one wants to receive abuse, spam or malware, whereas (depending on who is doing the censoring and who is being censored) maybe 30% to 50% of users want to receive the messages that the censor decides is "hate speech".
I think what you're actually saying is "I advocate for centralized platforms combating hate speech provided their definition of that term happens to agree closely with my own".
I'm worried about radicalizing the moderates, which is comparable to spam and malware, because (by definition) it's not content that the moderate was seeking out, even if it is tangentially related to the content that they were originally looking for.
I believe the Constitution is color blind. The words, "All men are created equal...", did not specify a race. The problem the right has the how the left tells them how to think.
This is where progressives go wrong. Stop telling people how they should think.
Frankly, I doubt the two sides are ever going to come to proper terms, and the best solution is just to give power back to the states. Then you can have libtard Portland and klan Mississippi, and people who don't like it can just move.
The only counter is to centralize with opposing points of view, because nothing fractured ever is sustainable.