EGT as a diagnostic tool
A few years ago flying home from visiting my parents, I noticed while in cruise flight that EGT on cylinder #3 started creeping up far out of its normal range (carb engine). The engine kept humming along without missing a beat.
Knowing that this likely meant an ignition problem in cylinder #3, an in-flight mag check was performed. Sure enough, when the left mag was turned off, the engine was clearly only firing on 3 of the 4 cylinders. Back on both mags, I made a precautionary landing at the nearest airport.
Because I carry a small tool kit with me that includes a spark plug socket, I was able to immediately follow the RH mag to cylinder #3, and found it was the top plug. I knew exactly which plug to pull within seconds of de-cowling.
Sure enough, the top plug had a lead ball shorting it out, which was quickly cleaned. Re-installed, test run, re-cowled, and back on my way home in less than 30 minutes from landing.
This is one illustration of the benefits of full EGT monitoring. Had I only monitored EGT on Cylinder 3, that could have led me down a much more tedious diagnostic path. Had I only monitored EGT on a single, but different cylinder, I would have flown on without knowing there was an issue until my next mag check prior to going somewhere. Again, diagnostics would be a bit tougher - perhaps suspecting a mag problem or pulling more plugs than necessary to find which cylinder was the culprit. CHT never changed, or at least not enough to notice. The cylinder was still producing plenty of power while it ran happily along with one spark plug firing.