Lawful interception requires things like paperwork, warrants, probably cause

Technically yes but there are back-room agreements to bypass this. I used to have warrants on my desk to set up call tracing in the 90's and eventually I was told to not require them any more and just leave test system and modems enabled logging disabled so agents could set up their own call tracing. The people I worked for had no skin in the game as they were all from the EU. I would be very surprised if this was no longer a thing. If anything I would expect it to be much simpler and more stream-lined by now, probably some HTTPS API end-point and some app on their phone.

In fairness to the agents some things are time sensitive like kidnappings / abductions. Provided logging is not disabled I think it is fine they have real time access if someone actually audits the logs and matches them up to incidents much like license plate queries by cops are supposed to be audited.