> "punish" hosts that carry the more controversial/risky content
Free speech is a completely different topic. If you're conflating copyright infringement and free speech when you're thinking about insurance, I can agree there's no way it could work. Let me clarify: coverage would be limited to copyright infringement claims only. Covering free speech with insurance is completely a non-starter, they would be opening themselves up to a new universe of risk, even suits directed directly at themselves. That said, the insurance company would be highly incentivized to discourage the abuse of copyright infringement laws to quell speech: these are separate concerns (from their perspective), so reducing such abuse would be good for them (and us!).
Think about what happens to controversial speech on centralized platforms now: some faceless moderator unilaterally decides -- without option to appeal -- whether to take your speech down from their platform permanently (it's their platform after all) and possibly ban you. In a decentralized platform you have the option to defend it with whatever resources you decide.
> Non-professionals are not just uploading home videos (which often contain copyrighted music by the way), they are also uploading stuff they have downloaded elsewhere (music, TV shows, etc). That's the key issue.
With a decentralized model like PeerTube you have to change your conception of who accepts and hosts uploads. You can't just upload to "The PeerTube" like you can YouTube, you have to upload to a federated instance. PeerTube makes hosting your own instance much easier and cheaper. Many will create their own, some might use one hosted by a family member, others might sign up for a more public instance. In each case, the instance will be more and more like the centralized model. But that's ok, because now there's a gradient. You have the choice to manage your own instance (or any available middle ground), with all the benefits and downsides that come with publishing your own content (except hosting costs of course, that's the point).
My point is that with this model, you have the choice to moderate it and defend it manually yourself (professionals, activists), or defer it entirely to a third party (basically the current centralized model). But there's a large gap between these, where some kind of insurance-like service could help bridge.