Why Full-Width, Half Max (FWHM)?

If you have two peaks with the same shape overlapping each other, they will
combine into a single peak with no dip between them (aka, no concavity,
assuming that the peak shape is convex up to the FWHM point) if they
overlap up to the FWHM.

While peak fitting could extract more information, the FWHM is a reasonable
bound on the simple ability to differentiate "features" or "structure".