There is no downside to using the resistor, but there is a downside to not using one.
When the EGT sensor is removed and no resistor is installed, it throws a CEL. This CEL can be blocked, but blocking a CEL does not change how the ECU reacts to a missing sensor.
The 2.2kOhm resistor tells the ECU that the EGT sensor is reading something like 800 degrees. This is a happy temperature and the ECU does nothing extra. With a missing sensor, the ECU will reference the highest temperature in the EGT tables and use a fuel trim to adjust. If you are un-tuned, or your tuner did not modify this table, it will mess up your fuel trims, possibly causing the engine to run funny or cause poor fuel economy.
By installing a $1 resistor, you prevent second guessing your tuner and stupid fueling issues related to a removed component.
I have never seen any reported cases of the resistor mod causing problems of any kind.