Why are 128kbit/s MP3s usually 44,100 Hz? Options

[eamon123]

Since 128kbit/s MP3s usually has a low-pass filter at 16,000 Hz, and the Nyquist-Shannon theorem states that all frequencies under f/2 Hz can be totally described at an f Hz sampling rate, why not encode at 32,000 Hz? Wouldn't it save more space?

[Dynamic]

Oops, thanks Robert. If I could edit my post now, I would. I missed that step out, it's the granules, not the frames that are divided by three. Nonetheless, the relative difference in short-block lengths is still that it's 50% greater length at 16 or 32 kHz than it is at 24 or 48 kHz and that it's the same for both 24 and 48 kHz.