[revelation]

There are various advanced approaches already to detecting IMSI catchers (and other nefarious network activity):

https://opensource.srlabs.de/projects/snoopsnitch

The basic problem with all of them is that the chip in your device with all the information, the baseband, is a separate high-powered processor running completely propietary software, and as such can not be modified to include protection or detection features. The app above only works with root access to a phone with a Qualcomm baseband that happens to have a diagnostic interface installed, which was then reverse-engineered to pickup the necessary information.

The situation is far, far from ideal if you consider that baseband chips will actively collaborate in compromising your privacy and run embedded systems that have never been vetted and are presumably vulnerable to any number of trivial exploits such as buffer overflows.