Author here. There are a few reasons, but the biggest one is simply the compression ratio.
The OG neural audio codec SoundStream (whose first author is Neil, now at Kyutai) can sound decent at 3kbps, whereas MP3 typically has around 128kbps, as you say. Interestingly, it was originally developed for audio compression for Google Meet, not for LLMs. Today's neural codecs have even better compression.
The more modern MP3 alternative is Opus, which can work ok at 12kbps, but it's still less efficient than neural audio codecs. However, these traditional codecs are a lot less CPU-hungry, so they have that going for them.
The OG neural audio codec SoundStream (whose first author is Neil, now at Kyutai) can sound decent at 3kbps, whereas MP3 typically has around 128kbps, as you say. Interestingly, it was originally developed for audio compression for Google Meet, not for LLMs. Today's neural codecs have even better compression.
The more modern MP3 alternative is Opus, which can work ok at 12kbps, but it's still less efficient than neural audio codecs. However, these traditional codecs are a lot less CPU-hungry, so they have that going for them.