White noise and entropy confusion about concepts
A signal's spectral entropy is not really a measure of information. Rather, it is a statistical measure of dispersion in the signal's power spectrum.

In other words, a random noise signal will tend to have large spectral entropy because its power spectrum is distributed among all frequencies. Speech signals tend to concentrate their power in a small number of bins, and their power spectrums are not flat. This results in lower spectral entropy.

A few comments about entropy:


Signals have information; sources have entropy. Signals never have entropy, and any reference to such concept is an abuse of terminology.
In communications, we prefer to have sources with large entropy, because then the messages that we transmit will convey a large amount of information. If you have a source with low entropy, then you should apply a source encoder to turn it into a large entropy source.
Shannon's entropy deals with uncorrelated sources. Many real-world sources produce correlated signals (such as text or speech) and their entropy is harder to define and calculate.