To me, it makes a lot of sense to grind your meat for burgers. With one exception, I haven't purchased pre-ground meat in a store for over 30 years. I just grind my own for burgers, or meatloaf, or, on rare occasions when I'm pressed for time, have my local neighborhood butcher grind it for me.
My rational for grinding my own meat is pretty simple. First, I've always been leery of exactly what goes into those packages of ground meat sitting in the cooler. I know that the meat is sprayed with a supposedly harmless chemical to help retain the reddish tint of fresh cut meat while it's on display, but I didn't know what else is included. Then, a few years ago, a fellow I knew, who was a reporter for the New York Times, did an article about a woman who suffered some serious consequences after eating a burger made with ground meat produced by Cargill, which makes 80% of the ground meat in the US. Confirming my concerns, that article sealed the deal for me.
https://www.nytimes.com/2009/10/04/health/04meat.html
Second, my preferred mix for burgers is an equal blend of chuck, brisket, and short rib meat. Unless you find a very high end (high cost) purveyor of a similar mix, you're not going to find that at any store. Naturally, I always try to stock up when I find those cuts on sale, but that doesn't always happen.
Do I save money by doing what I do? I don't know, but I'm comfortable in doing what I do with both food safety and a great tasting burger in mind.