Like you said, the main benefit is control. I'd say the two main variables you're controlling for are amount of fat in the mixture and the tenderness and quality of the cuts used. Depending on the application, you might use a different mixture of meat. (For burgers, Alton Brown uses a 50/50 mixture of chuck and sirloin.)
Grinding your own could also be considered a play for increased food safety. If there are any bacteria on the surface of the cuts of beef that go into the grinder, they will be pretty well distributed throughout grind. The longer (and warmer) the ground beef is stored between when it is ground and cooked, the more chance that the bacteria could grow to sufficient numbers that they could do some serious harm to the consumer. This is why it's recommended that ground beef is cooked to a higher internal temperature than say a steak. In grinding, everything effectively becomes surface area so you have to cook a burger all the way through to be sure you've killed any bacteria.
If you're grinding you're own, you can make the interval between grinding and cooking arbitrarily short, so if you want to take your chances with a rare burger, this would probably be the best reason to grind your own. You're still running a risk in this case as any bacteria that were on the outside of your meat are now on the inside of your burger and won't be killed if the meat is left rare. You would just be trusting that the butcher did a good job of keeping the outside of the cuts you purchased relatively free from infection. Also, any food safety benefit assumes you're doing a good job of cleaning your equipment. Meat grinders can be a real PITA to clean well.
As far as the flavor difference is concerned, I would assume that to be minimal, again if you control for any difference in quality and cuts of beef that might be used. If your butcher grinds the beef and stores it cold in a case or wrapped for a day or two before it goes out the door the flavor shouldn't change enough that you'd notice it after seasoning and cooking. Oxydation would have had a chance to change the color of the meat over that period, the reason why ground beef can look brown on the outside but still nice and pink when broken up. But there shouldn't be enough time for there to have a marked effect on the flavor.
If there is any perceptible flavor difference you'd probably notice it more in a burger where you're tasting the meat by itself for the most part than in something like a chili or stew. (As an aside, you don't necessarily need to grind all the meat in those anyway as they tend to be cooked long enough to soften bigger chunks of tougher cuts.)
The Chinese use what is often referred to as black beans, but they're actually fermented soybeans.
Azuki/Adzuki beans are the beans used in red bean paste. Most often, they're sweetened and mashed. But I don't see any reason you can't use them in Hoppin' John. I'd temper the slight sweetness of the azukis with a bit of black bean paste to give a more savory flavor. (The barbeque'd pork is already going to be a bit sweet.)
Best Answer
Ground beef does not work well in any traditional stir-fry or soupy dish, though there are probably one or two that actually call for it
But it does work well, and is actually used in China for stuffed items. Some deep fried or steamed pastry rolls ("dim sum") or steamed buns have some ground beef in the filling
In my experience it was a very coarse grind, and unlike the typical western butchery grind
I have seen a form of a "scotch egg", and hard boiled egg, wrapped with a smooth layer of chilies, herbs, and ground beef, and baked until set. Served cold, but very hot!
It is also used for some kinds of BBQ skewers (kebab style), more predominantly in the Muslim areas (which are limited). Some skewers are actual edible vegetables; like stems of choy sum, or a sort of asparagus etc. All very nice!
Of course, you can get all this in Pork, Chicken, Lamb, Goat, or whatever else moves in China
Examples
Beef Roll (like an English 'Sausage Roll' with light pastry)
Beef "String" (on right, like middle eastern kebab, but totally different herb taste)
Beef Steamed Bun