If you have the Doctor carrying around a mobile, he's far too easy for people to call up for help,

I can't argue with your external story logic, but I'm a stickler for in story reasons, if it hadn't been for Boom Town I might have agreed that the Doctor didn't want to be tied to his phone so didn't have one (the TARDIS phone I suspect is only reachable by certain people at certain times, and the one on the door isn't a real phone). But in BT it worked so nicely for having the tam spread out that it's hard to imagine he wouldn't want a way to keep tabs on certain companions who have a tendency to wander off, and he could have been useful to Donna.