The latter one is about to change, at least for certain non-vital topics. We see privatization in law enforcement for copyright, free speech / personal rights, and so on.
When Facebook marks "fake news" or handles "hate speech", and when Google/Youtube removes "copyrighted material", there is neither the police nor any judge in the loop. Also, there are often false positives such as removing creative commons videos with no clear path to dispute.
There will soon be laws that require companies to interpret the law, which is a very worrying trend.
Let's not forget forced arbitration. Companies that wrong you can now deny you your day in court if they just add a forced arbitration clause into the fine-print. They are removing conflicts from the justice system into a private system where the incentives are much more murky.