Nothing is "impossible" to trace. What you're describing would certainly be difficult to track down, but not impossible.
In the early to mid 1990s Kevin Mitnick tried an analog version of what you're describing, with cloned cell phones and a cellular modem in place of modern digital mobile networks. Since he could change the cellular ID of his phone at will to another ID (and did every day), this is arguably less traceable than your scenario where there's a single subscriber ID associated with the mobile device. Mitnick also regularly conducted his own intelligence campaign against the police trying to catch him, going as far as to tap the conference calls of the FBI.
And yet with all this, Mitnick was caught (albeit with a large amount of effort fueled by media hype). He was eventually traced through his dialup access through Netcom, and physically traced to his apartment in North Carolina through directional radio. This was not a small amount of effort at the time and required a team of experts to accomplish, but it still happened.
These days there's no dialups, but we do have much more logins to services that never existed in the 1990s. It's certainly possible to use the same approach, and eventually trace back to a physical location to apprehend a suspect.
The point being, that given enough attention and effort, anyone can be tracked. There's always some leak of information somewhere, given enough time. Most recently Ross Ulbricht (creator of The Silk Road) was caught,not long ago Bin Laden was caught, and in the 1990s Unabomber Ted Kazinski was caught. All of these people carried out remote crimes and thought themselves to be invulnerable, but all were eventually tracked down from flaws in their own stealth.