This is the brave new world. The free-market of information is beginning to show its teeth for better or worse and those who shy away from it will lose market share.
Philosophically, I agree with you, but I'm not sure if it really will work that way.
In fact this whole brewhaha was started because the current head of the WPP said he wanted Google to do something about his ads showing up next to extremist videos. It's not inconceivable the article on The Times that started it all was made as part of WPP's strategy to make Google kowtow to them on this subject.
Basically don't underestimate the power of advertising agencies. They can produce news cycles at will.
Economic politics is for the government and society to play with, not individual mega-corps.
Created by harming others? Same. Is a threat to society? Same. Goes against cultural norms? Almost same (those in the US are far more accepting of fake violence, but real videos of people being murdered tends to be quite taboo).
One includes violence, the other includes sexual violence. But any argument for banning or allowing one seems to be a very close fit to the other.
Content classification is something you must do if you're a major content provider in the US, period. Saying someone should just "let the advertisers sort it out" means you're not addressing the type of content classification we're discussing here: per-user, not per-advertiser. Porn & CP are extreme examples, but so are violent extremist videos.
The Fifth Amendment is now getting killed at the federal court level, and I'm not sure what are the chances for the current or even future Supreme Court setup are to revert this.
And now we're watching the First Amendment die in slow motion, too, both from attacks of the current administration, which basically says that the 1st amendment is a bad thing and "makes us weak", as well as from all the different groups out there who seem to "take offense" for everything that happens, and want to be in "safe spaces."
And because the media is consolidated in a few large companies and all they care about is profits, it's easy to take down content that "offends" various groups.