When should I use a frequency spectrum rather than a spectrogram representation?
The spectrogram suffers from a time/resolution restriction - the smaller your time step, the smaller your analysis windows become, the worse your frequency resolution gets.

It is a waste of frequency resolution to break down a stationary signal into tiny temporal slices. Thus, if you know in advance that your signal you analyze is stationary; or if you have pre-segmented your signal into stationary segments (using a transient/onset detector; novelty detection; or an auxiliary signal/sensor), there is no reason to lose frequency resolution by using the spectrogram.