If the clock rate can be corrected by a factor, then it is a matter of calibration. We engineers need calibration because we don't want to understand all the details. You physicist may be able to predict what will happen without calibration, but how do you know if it is correct, like nutrino velocity measured in CERN?

I think general relativity is about 200 years too advanced for human being, that is why during the first 100 years we couldn't find much use of it. Without it, we would gradually find some facts that are quite confusing, the unexplainable error of atomic clocks is one of them.