Of course, right?
Look, you can buy ground beef from the supermarket if you want. I ate that stuff my whole life, and I'm still alive with a perfectly functioning liver.
But it looks like a mass of pink maggots, doesn't it? It just looks nasty. And you can never tell what's mixed in there. Bleh. Store-bought ground beef *has* to be cooked until it's well-done. It's not safe otherwise.
Sometimes I like a burger to be rare. So I grind it myself.
I have a hand grinder, but I use it for pork sausage. I don't like to mix pork and beef grinders. The beef I do in my food processor.
Chuck roast is best for this, but I've used leaner meats when they're on sale or I'm feeling self-conscious about the extra me around my middle. But really, chuck is the best choice. Cut your roast into lots of small pieces, maybe two inches around. The size doesn't matter too much; the larger your pieces the more you'll have to process them.
Put about a third of a pound to a half pound of meat into the machine and pulse it until it's ground smooth. Start with 12 pulses and check it. It may take as many as 20. You may be tempted to just turn the machine on and run it, but the meat turns into cow mousse pretty quickly. If it's pink and airy, it's not going to hold together the way a good burger should.
Then you grill or broil them. Or fry them if you must.
More on toppings later.