It's a power everyone has. You should read Habermas (https://en.wikipedia.org/wiki/Public_sphere). The entire purpose of civil society is to draw the boundaries around what's acceptable and create the norms that allow people to work out their differences.
Allowing your public sphere to be filled up with people hostile to the concept of being able to work out their differences leads to a breakdown in social order and the rise of totalitarianism.
Absolutely, but I'm not sure that's germane to this topic. That's an argument for why we should have open standards and be opposed to monopolies, it's not an argument for not having moderation.
As it stands though, many social networks are dominated by the perspectives of a minority of technically savvy people with an abundance of free-time and a willingness to spam propaganda. They get away with it because these social networks were designed as ad platforms, so spamming propaganda in peoples' faces is literally why they exist and they don't want to invest too many resources into letting you control who gets to shove things in your face and who doesn't.