Merits of "Zero-Phase" Zero Padding
This is just about obtaining a symmetric signal after zero-padding. Take a symmetric signal (w.r.t. to time index $n=0$) and append zeros. Due to the implicit periodicity of the time signal used as input to the DFT, it does not matter if you append all zeros to the right, to the left, or on both ends of the symmetric signal. In any case, since the DFT/FFT assumes the first sample in the buffer to be the time origin, the input vector to the FFT needs to be arranged as

[right half of the signal | left half of the signal]

which is basically one period of the periodically continued zero-padded signal between $n=0$ and $n=N-1$, where $N$ is the FFT length, i.e. the length of the signal after zero-padding. Note that now all the zeros end up in the middle of the vector to be transformed. If done correctly, the result of the FFT will be purely real-valued (apart from numerical errors). If the signal is asymmetrical, its FFT will be purely imaginary.