If they receive a notice that there is illegal content, that it should be removed and then refuse to cooperate?

Then yes, e2e is not under fire, not cooperating in moderating/Removing known criminals is

He was not arrested for privacy, there are huge open groups on Telegram for piracy, csam and cyber criminals.

These groups are not encrypted, everything is stored in plain text on their servers. He is being arrested for not removing/moderating this content.

Problem is that some companies double dip. Pay for the service and have your data sold.