That one is actually because it's two different words:
"people" is the plural form of "person", i.e. one person, two people, as a group
"people" (pl. "peoples") is a group of people as a unit, e.g. a tribe or an ethnic group or the citizens of a country
"persons" is ALSO the plural of "person" but only used when you talk about individuals rather than a group (e.g. "person of interest" -> "persons of interest", not "people of interest")
Yes this is a bit awkward and yes sometimes what's grammatically possible still sounds awkward even to native speakers (e.g. I'd argue "the polices" is a legitimate term when discussing multiple police organisations of a country as an abstract group but it sounds extremely wrong to most people apparently).