Is a Cessna 172S still airworthy if factory-installed instrumentation not required for day VFR flight is inoperative? A C172S I occasionally rent had the EGT gauge placarded INOP when it had a JPI EDM-700 engine monitor installed. The placard sits on the gauge so you can no longer see the needle. Probably the single point EGT probe has been removed so the needle wouldn't work anymore. Of course that is fine - the EDM-700 is TSO'd.
Now recently the EDM itself is placarded INOP and its circuit breaker collared so it cannot be reset. 

So now this 172S has two INOP EGT gauges, and I'm down to leaning by ear. I know the EGT gauge is not required daytime VFR equipment. However, since the airplane was certificated having a factory EGT gauge installed, I'm wondering whether it's airworthy like this. The Plane is N-registered and I'm asking within FAA jurisdiction.
Part 91 does not require an EGT probe for any operations so the next thing to look at is your AFM.

Your C172S has an AFM that includes a Comprehensive Equipment List. It is probably similar to this one that indicates that the EGT probe is standard equipment—not required for certification, this airplane can fly with it placarded.