> If "platforms [were not] legally bound by them" wouldn't that pose some serious difficulty for legitimate takedown injunctions?
The naming here is potentially misleading and contributes to the confusion. The "takedown injunctions" referred to are not orders by a court to an internet service to take down content (such injunctions can be issued in cases where the internet service is a party, and absolutely are binding.)
Instead, they are injunctions issued in cases where the creator of the content is the defendant (in theory, at least) and are directed at that creator to remove the content; they are then often used by those who initiated the lawsuit to support a request to the internet provider to take the content down.
If an internet service refuses to take down content that really violates some person's rights, a lawsuit against the internet service which generates an order directed against that service to remove the material is always an available means for a mandatory take down, that isn't in dispute.