Frequency response of a long signal
Assuming that the system response is smooth, without narrow peaks or narrow valeys. And that the spectrum of the input signal does not vary so much from one chunk to another.
I think this approach is better than doing a single FFT, as you know the FFT of a random signal will have lots of randomness. Averaging may also remove effects due to quantization errors.
Since the FFT bins are equally distributed in the spectrum, each bin corresponds to a very narrow band of your spectrum, and the energy in this band is highly dependent on the signal you used, or noise, if the FFT is big. In order to have a smooth curve you can compute the energy in a wider band by applying a moving average, for instance.