dft - Frequency-domain zero padding - special treatment of X[N/2]

Suppose we wish to interpolate a periodic signal with an even number of samples (e.g. N=8) by zero-padding in the frequency domain.

Let the DFT X=[A,B,C,D,E,F,G,H]
Now let's pad it to 16 samples to give Y. Every textbook example and online tutorial I have seen inserts zeros at [Y4...Y11] giving
Y=[2A,2B,2C,2D,0,0,0,0,0,0,0,0,2E,2F,2G,2H].
(Then y = idft(Y) is the interpolated signal.)

Why not instead use Y=[2A,2B,2C,2D,E,0,0,0,0,0,0,0,E,2F,2G,2H]?

As far as I can tell (my math knowledge is limited):

• It minimises the total power


• It ensures that if x is real-valued then so is y



• y still intersects x at all the sample points, as required (I think this is true for any p where Y=[2A,2B,2C,2D,pE,0,0,0,0,0,0,0,(2-p)E,2F,2G,2H])

So why is it never done this way?

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Edit: x is not necessarily real-valued or band-limited.