IMHO
taxy - "to loosen a thick sauce" is the expression commonly used of pasta water, (plus it can add a richness to stews/soups of other than pasta).
Your sauce will stick better to your pasta if you don't rinse it, not if you add the starchy water back to your noodles, it's probably too late. If your noodles are thick and sticking to each other along with a thick sauce then adding pasta water to "loosened the sauce" would be necessary to help.
But which or what ever the reason - I have never found it necessary. When I did hear of it I did start saving the water but LOL... always ended up tossing it.
Of course, I used it the few times I ever made a carbonara which was only when I got into more cooking things. I'd never even knew what carbonara was until 10/15 years ago.
medtran - I have never made a soubise. Looked it up, very interesting! Lately have been watching video's on different sauces and been thinking I should start teaching myself - go thru the lists!