You think this stuff is just anti-terrorism? The whole reason I even MENTIONED the idea of a warrant is specifically for normal policework. It's the same as searching someone's house after a murder's taken place- just now, instead of reading their files, it's all in a secure place in their computer.
Having a reasonable way to read that stuff(WITHOUT USING A BACKDOOR. I don't want weaker crypto just for this- but businesses hosting this stuff always have their proprietary ways of handling things) is just a continuation of previous law.