FFT radix-2 in audio - resolution issues - logarithmic scale - sample rate VS buffer size
If you overlap, you can refresh an N long FFT every sample, or every M samples, no need to wait an entire 1 second, or for N samples.

No need to find a sample rate that is 2^n, as most modern FFT libraries support any reasonable product of several small primes.

For analysis, no need to use the same size FFT for both low and high frequencies (or mid, or upper mid, or an entire octave, etc.)

Why FFT?  O(NLogN) provided a speedup that in ancient pre-history allowed DFTs to be run on chips with far far less than a few million transistors, and today still allows real-time performance on power sources that fit in a watch or hearing aid or implant.  Could even allow some Fourier analysis of data when computers were women who used paper and pencil.  The square matrix derivation of a DFT requires less chalk on the classroom chalkboard (today: less iPad scrolling) than more modern audio tricks.

But if you have a larger power source with modern hardware/chips/iPhones, you can use piles of wavelets, large filter banks, psycho-acoustic models, Goertzels, and several other algorithms that are far less efficient than an O(NLogN) sped-up DFT, but together can still easily run faster that real-time requires.