numerical integration – Shouldn’t NIntegrate return a number whose precision is PrecisionGoal, not WorkingPrecision?

I know that Mathematica has great built-in precision tracking, so when you do calculations with arbitrary-precision numbers, Mathematica keeps track of the precision on the result. Given this careful attention to numerical error and precision tracking, I am surprised that, say

InputForm(NIntegrate(E^(-x^2), {x, 0, Infinity},PrecisionGoal -> 20, WorkingPrecision -> 100))

returns a number with precision 100, not 20. I know Mathematica is using precision-100 numbers in its numerical calculations for NIntegrate, but the function is built to return a number whose actual precision is at least 20. In the spirit of useful precision tracking, wouldn’t it make more sense for NIntegrate to return a number with a precision of PrecisionGoal, not WorkingPrecision?

This question is more about numerical coding philosophy than about how NIntegrate works. But this is important as Wolfram presumably makes these decisions with use cases in mind, so I want to know if I’m missing something.