Like and Dislikes are only as valuable as users allow them to be. A great counterexample to many of your arguments is the social media site we are discussing this topic on. The culture on Hacker News de-emphasizes Likes and Dislike. Comment karma is visible to the poster, but to a reader, a +100 karma comment is equal to a +4 karma comment with the only difference being what is seen first. I personally forget about that and end up reading comments to the end of threads I enjoy anyway.
I think letting such hostility build for the concept of social media is as damaging as any political extremism the censorship is supposed to combat. It feels like the extremism isn't gone, just redirected. Social media and the internet has changed who people interact with, not just how. In the past extreme ideas existed, but were tempered because of others around them. Social media has allowed people to choose to only listen to people with the same perspective, letting extreme ideas go uncontrolled. You can argue that it's the fault of the technology, but the main responsibility falls on the individuals.
Social media doesn't make people hateful, it makes it easier for hateful people to convince other to think like them. Bullies have existed long before social media and continue to exist in every context.