How important is it to use power of 2 when using FFT?
Modern FFT libraries, such as FFTW and Apple's Accelerate framework can do non-power-of-2 FFTs very efficiently, as long as all the prime divisors of the composite length are fairly small (2,3,5,etc.)

A power of 2 makes it simpler (about 1 page of source code) if you have to code your own FFT for some reason, or are otherwise constrained as to max program length (or FPGA gates, etc.)

For phase measurement, it might be easier to do an fftshift (pre-rotate the data by N/2) to reference FFT phase to the center of the data window, where the evenness/oddness ratio, and thus the phase won't change or alternate with bin number (for phase that is the same at the center of that data window) even for signals that are non-periodic in the FFT length, as you vary the length.