The two problems with this approach:

1. Even if the courts always get it right, small sites are not going to want to want to hire a lawyer and go to court to defend someone else's speech. They will instead err on the side of caution (as many do now for DMCA violations), causing a chilling effect on speech.

2. In a system where whether a platform is liable for its content is ultimately decided by courts we cede a lot of power over speech to the government.

I really don't think the courts are the path we want to take.