Huygens' principle seemed quite complete in this description if applied correctly. I noticed that Fresnel was credited in the Huygens-Fresnel principle, as well. I think it is because he was able to describe diffraction with the principle correctly, something Huygens could not do in his lifetime. The correct description of diffraction using Huygens' principle took ~120 years after Huygens' death. It is quite curious to me.

Why couldn't Huygens explain diffraction using his principle?