But it's not necessarily that the system is "correct", it's more like it allows you to make falsifiable predictions. Say you want to track the health of a culture over 1000 years, or of several cultures based on a certain variable (like degree of deforestation, or climate). In order to have anything other than subjective opinions, you need to have an objective measuring stick that can be reproduced by other people independently.

You may chose average lifespan, child mortality, average daily calories, put them in a weighted sum, and track that.

It doesn't make it The correct measure, of course. But it's something that anybody else can try and check independently, and instead of saying "deforestation sucks for health" you'll say "the health index took a steep dive 50 years after the last tree was felled on Easter Island". That's falsifiable - somebody else can do the math and say "no, it's wrong: people lived longer and ate more, with less child mortality".