Why can't you just take the DFT itself? And how accurate is this method in spectral density estimation? Are there cases in which it is very accurate?
Many applications just want a strictly real value of some sort (for a simple line graph, or peak magnitude frequency estimate, etc.). And the modulus squared is a real value; whereas the result of a DFT is a complex valued vector. (except, depending on definitions, for strictly even functions/waveforms)