The case you are speaking is when we have a very short loop in a sample and the problem if we duplicate this portion several times is that both the autocorrelation and the Fourier transform will tend to give a resulting frequency equal to the loop length.
For example if we select a loop comprising 224 points with a sample rate of 44100 (as shown in your example), the length will be 5.08 ms and we will have a perfect correlation (since we duplicate the portion) at the frequency equal to 196.875 Hz.
If we add un single point, a loop comprising 225 points will have a length of 5.10 ms and the perfect correlation will be 196 Hz. The difference between 196.875 Hz and 196 Hz is 8 cents of a semitone.
All this to say that the result will be too sensitive to the number of points included in the small loop.
I may not be aware of all mathematical tools but based on the small loop we provide, extending both limits (start and end) provides a simple and better base to study the harmonic content.