Is it silly and why is it silly to automatically set the Federal Funds Rate to be a mathematical function of recent CPI, PPI etc?
First, no matter how you set interest rate, as long as you take CPI into your decision making, even if the decision is completely subjective it will be some function CPI etc.
For example, suppose that Fed committee select federal funds rate purely based on their subjective feeling of whether CPI is high or low, without any recourse to any economic theory whatsoever. Even in that kind of scenario we can write:
$$FFR_t = f(CPI_t)$$
Hence even pure subjective thinking will result in FFR to be some function.
Second, I am guessing that your underlaying question is whether Fed should commit to set FFR according some publicly known function without human interference. There are some optimal rules such as the Taylor rule where central bank is supposed to set interest rate according to the following function:
$$i_{t}=\pi _{t}+r_{t}^{*}+a_{\pi }(\pi _{t}-\pi _{t}^{*})+a_{y}(y_{t}-{\bar y}_{t}).$$
where $i$ is FFR/interest rate, $\pi$ inflation (change in CPI), * denotes inflation target, $r^*$ is the real interest rate and $y$ is output and and bar denotes the output at full employment. Finally, $a_i$'s are the parameters that tell us how central bank wants to care about inflation and full employment.
The problem is that Fed cannot know what inflation (or even CPI), real interest rate, real output or its natural level are. Take real output for example, the first estimate for real output comes with about 1-2Q lag, and then that estimate will be revised numerous times and true value will be known in about 3-6 years. That is why research often works with vintage GDP data, and that is why sometimes we might even think there is recession and five years after discover GDP was positive all along.
This is why any function that depends on macro parameters can't be easily practically implemented. Even if Fed would like to always follow Taylor rule, and even if it would be content to just use the earliest estimate, it would mean it can never react to economy in real time which would be very constraining.
Moreover, different Fed chairman and committee members might have different ideas of how Fed should care about inflation and full employment. Some might prefer more monetary stability, others might prefer to make sure economy always runs at its full potential. Economists, and society in general will disagree about these goals. You would want a system where Fed has some flexibility to change as concerns of society change (for example, some people nowadays even advocate Fed policy should be set to combat climate change).
As a consequence it is practically impossible for Fed to have any rule for its interest rate that would take into account inflation and full employment (as its mandate says it should).
