I have seen bratwurst burgers. That’s fundamentally a ground pork burger with a few seasonings ground in.
I haven’t eaten one, though. I still prefer the snap of a good natural casing in my bratwursts.
Not burgers, but I made Swedish meatballs with bison and emu. I was hosting a dinner and the foods we had were those mentioned on the show Babylon 5. Swedish meatballs were what G’kar made when he couldn’t get the Narn ingredients for breen.The recipe required lean red meats and I wanted something exotic to fit the theme.
A good burger has 20% fat. To me, a great burger tastes good even if just eating the meat. I have no problem adding egg, spices, feta, or whatever is needed to the mix. It’s all in the result, but usually burger makes me think ground meat.
I often make gyros. It’s very easy and healthy and as good as at a restaurant. But because I bake it then slice it thinly I don’t think of it as a burger unless I make a patty out of it and fry that.
Veal, bacon, lamb and salmon all work well; sometimes mixing the first three with medium beef. Pork is sometimes good. Specialty meats in my experience are just okay and rarely worth the hype and cost; though I have not had anything very exotic (except I have eaten at a Chinese night market).
I prefer far less fat. When I make a beef burger I use a lean steak, trim off any fat, then grind the meat. I form a large patty which I season, partially freeze, then vacuum pack. I sous vide rare, torch sear, and serve it on a bun with condiments on the side.
It’s not that lower fat can’t make a tasty burger if you use novel cooking methods and fresh grind. But a lot of the flavour of meat is in the fat. Most people who make burgers grill or fry them, which tends to dry out extra-lean meats. I add olive oil if not using regular or medium ground beef or its equivalent.
doesn’t Johnsonville sell Pork sausage burgers?
doesn’t Johnsonville sell ground pork sausage burgers?
Yes, they do, as I noted upthread, in post #38:
Concur. I do not notice any better flavor with higher fat, just more grill flare ups as it cooks off, making my nice even pink harder to achieve…
I’m looking forward to it.
The author of the “Meat Hook Meat Book”, written by a master butcher, says it simply. “It’s no fun without the fat”.
That’s the best part! 
I do feel that more fat adds a richer flavor, so 80/20 for me is ideal, with 85/15 being workable. I think the above though points to one of the areas of dispute: cooking methods. On a grill, dripping fat can cause difficulties in controlling flame. In sous vide, you are extremely unlikely to end up with a dry burger even with low fat. But since I do 90+% of my burgers in a hot cast iron skillet, the medium high fat I suggested above is perfect.
Doesn’t dry out, almost no risk of flare up, and the fat (plus a little in the pan to get it going) results in an evenly crispy top and bottom while allowing for a perfect medium burger.
So your fat choice, regardless of meat critter, is going to be strongly influenced by your cooking method.