If you’re already doing raw sausage there probably isn’t a reason you can’t do raw ground beef too.
With that said, we’re a raw sausage place but we still pre-cook our meatballs and dice them. If I was doing ground beef I would probably pre-cook that as well. We’re known for our home-made sausage and I would never do that any other way… but I don’t think I would judge a ground beef topping to be nearly as important as to add in the additional time required to apply it raw to the pizza.
I’d precook it so we could throw it on the pizza fast. If you’re going to pre-cook it, cook it all the way the first time. Not cooking it to a fully safe level the first time could cause a problem when you cook it on the pizza… It may look done on the outside, but the inside still hasn’t hit a full safe temperature.
To answer your question about doing both, we don’t. When people ask for ground beef we just say “we have home-made meatball, will that work?” Considering I’d probably season the ground beef pretty similar to how I season meatballs I don’t think there’s much point in having both on the menu.
For chicken, we use pre-cooked out of a box. We already handle raw chicken with wings so I’m not concerned about handling, but the bought-in stuff just seems to be better than anything I can consistently bake in my oven. If I had a grill I might change my mind on that though.