protections we put in place to secure players’ data, remove illegal content, and combat unsafe community content would not exist

Nanny State BS. If someone runs a private server, it’s their responsibility to moderate it.

and would leave rights holders liable.

No it wouldn’t.

In addition, many titles are designed from the ground-up to be online-only

Unreal Tournament games are online or multiplayer only games. Even though Epic shut down the master servers, you can modify the .ini file to redirect to a community server. “Online-only” translates to predatory monetization models.