I wouldn't put it in carbonara, but Marcella Hazan's recipe[1] includes it and she's about as big of a "pasta sauce authority figure" as you're likely to find.
[1] https://www.latimes.com/recipe/marcella-hazans-spaghetti-car...
[1] https://www.latimes.com/recipe/marcella-hazans-spaghetti-car...
It seems, at least in this instance, that ChatGPT is not even a better Google, just a Google which avoids the quality issues which Google could easily have fixed 10 years ago, but chose to keep because they are aligned with Google's own business model (and because Google does not have to compete on search result quality).