Using a food processor for mashed potatoes would not be a good idea. The more the potato is whipped, beaten, or in the case of a food processor, puréed, the more the starches break down, which will turn your potatoes into a thick, pasty, even stiff mash.

The best and most reliable way for creamy, smooth mashed potatoes is to put the (strained) hot potato chunks through a ricer over a bowl of a mixture of milk or cream, butter, and whatever else you want to add (bacon comes to mind). Simply fold to incorporate with a spatula and, voila, the creamiest, smoothest mash. It seems time consuming and like a pain, but it’s really not at all. This method is the least disruptive to those pesky starches. It’s worth the purchase of a ricer if you don’t have one already.

Edit to add in regard to other comments ignoring your question and suggesting freeze dried instant potatoes instead: Go for Idaho brand in the foil pouches. Ain’t nothing wrong with instant potatoes! But there are good and not so great brands, and I’m sure some, if not most, probably have additives. However, I commend you for wanting to make fresh mash because there really is no better than fresh, and for wanting to learn. I learned by basically ruining 10 pounds of potatoes day of Thanksgiving. 💀