The former cases seem unlikely, so what is the difference with YouTube?
Yes, and they already set standards for the channels they accept on their cable platform.
> Can my cell phone carrier censor whatever conversations I have that they don't like?
No, your phone carrier is a common carrier.
> Can Google skew and eliminate searches they don't agree with?
Yes, but they might hit issues with advertising guidelines depending on intent
People get upset when content is censored which they view to be vital to the public interest. In the case of particularly gruesome combat footage or violent crime I don’t see how in some jurisdictions those sites could operate with the content NOT taken down. For instance, you recall how 8chan was taken down over the Christchurch NZ shooters manifesto and video.
This is already the case per the safe harbor.
> Illegal forms of pornography would have to be the litmus test here.
Note that being not liable is not the same as being immune to takedown. Youtube isn't legally liable for what you post, but they still have to comply with the law (and they are liable if they fail to comply).
> People get upset when content is censored which they view to be vital to the public interest.
Youtube isn't censoring material because of legal liability. Youtube censors material because their investors and advertisers don't want some materials on Youtube which they perceive to negatively affect is, such as combat footage, material seen to be preying on children and anything with nudity.
There are no such limitations on YouTube, Twitter, nor are there restrictions on competition.
If my ISP is down I can't watch TV or check my emails. If Youtube is down for an hour I can still shitpost on HN until it's back up.
YouTube, as a private entity, can choose to do whatever it wants.
A main motivation behind PageRank was dissatisfaction with the quality and content of other search engines. And Google's SERP algorithm has constantly changed and evolved over the years.
They have been doing that for a while.
One could possibly blame it on poor engineering and bugs, but given Google's talent pool, that seems unlikely.