Why did they need the spectrogram?

Not everything is AI, they provided the spectogram. Even a trained eye can read one, especially if context is provided.

Like Scott Manley says, going from a frequency domain image representation to a time domain sound file is something that is extremely old and does not and has not required AI the last 50 years. It's just that they vibe coded the extremely old, extremely normal algorithmic solution. AI did not recreate the dead pilots voice, it just made data preparation and coding a bit less work.

It's almost certain you've used software or seen/heard software output today that transformed between frequency domain and time domain. It's ubiquitous.