What is the purpose of dividing an audio signal into segments and analysis each segment?
Analyzing signals per segments, with proper windowing, is a way to cope with non-stationary in audio samples.  With full-size analysis, features can get mixed. Segment-splitting is thus at play in many algorithms (mp3, shazam).
The length of window is often a matter of trade-offs, between data information and computing advantages:

signal sampling (window length is quite meaningless without sampling rate), with respect to the following:
analyzing or extracting informational content from the signal: various ranges of stationarity may exist in the data, or generally useful processing features,
easiness in computing: the power-of-two length you mention can be beneficial (faster algorithms like in the FFT), parallel computing, dedicated hardware, closer to real-time analysis.