There's just no theory of free speech that would require google to run ads on white supremacist websites. After all it's the advertisers that don't want it, and they don't want it because the backlash would end up hurting them, on balance.
All that means that this sort of content simply doesn't have any value as a vehicle for mainstream advertisement. It's actually quite democratic in a way, because the value originates with the broad public. If everyone starts only buying cars advertised on strangulation porn sites tomorrow, the money would follow.
Until then, I'm quite happy at current arrangement: There's a few Silos "policed" to different levels of sensibility, then there's the almost free-for-all web, and governments largely don't play a role. The big advantage of private companies doing this (even if intransparent), is that there are several of these companies, and that none of them have an army.
P. S/:Please let me know where these shadier parts of Facebook and Youtube are, because I don't think there's much there, beyond some vintage softporn.
The vast majority of people are not going to Youtube, Twitter, or Facebook to watch dog killing videos.
These companies have just been hiding behind the free speech folk with their heads buried in the sand about the long term effects of all this content.
If we can figure out ways to get our govts to tell us know how many policemen we need and the process it takes to become one, there is no reason Silicon Valley should be doing this vital policing in secret.