They … did, though?

You're presumably referencing Missouri v. Biden, to which the EFF did file an amicus[1]. In it, they note,

> Many platforms have potentially problematic “trusted flagger” programs in which certain groups and individuals enjoy “some degree of priority in the processing of notices

> Of course, governmental participation in content moderation processes raises First Amendment issues not present with non-governmental inputs

With their overall opinion being something like "content moderation is normal, the government flagging content is also normal, and there are instances where the government's flagging of content moderation can be fine & not run afoul of 1A, but there are instances where it can, and we urge the court to think"

Note in this case, the platform was removing the content. The government was, in one respect, merely asking. (There were assertions that in other instances, such as public statements, the case was less so.) The court eventually ruled, and the ruling I saw from the 5th circuit seemed reasonable. (I think that was a preliminary injunction. AIUI, the case as a whole was never ruled on, because the Trump administration took over.)

[1]: https://www.eff.org/document/missouri-v-biden-amicus-brief