What is the role of butter in mash gravy? [closed]

I am making a gravy for mashed potatoes. Looking at recipes online, I have found that a few of them don't require any butter, while others use them to varying ratios (to broth/water)

What is the role of this ingredient in an excellent gravy for mashed potatoes?

I thought of two:

Fat. Butter is rich in fat, and the increased fat in gravy helps it to coat and stick to the starchy molecules of the potatoes better, so they come together better in each bite.
Thickening. The oil in butter and the broth used in most gravy come together as an emulsion of sorts, like the way mayonnaise is made. This helps to thicken the gravy.

Best Answer

The most common purpose of butter in gravy is for a roux, which is a thickener made from cooking flour in fat. Stock/drippings alone would be too runny, so it is thickened to make it more convenient to eat with the mashed potatoes. If the recipe doesn't call for a roux, it probably uses cornstarch as the thickener. Using cornstarch would be a slightly healthier option (no additional fat) and doesn't impart a flavor, while a roux can add a slightly nutty taste depending on how long its cooked.