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.)
For my part, I suggest you explore the wonders of Spaghetti, and that most American of dishes, the "Sloppy Joe."
You can try adding binders like egg and/or peanut butter (or bananas if you're vegan, har har) in order to firm up your beef for pan frying (forget the grill, it ain't happenin), but, while that will help, it'll definitely change the flavor...possibly for the better. I've been known to add those things to regular ground beef (Also, applesauce, which will not help your problem here, but is quite tasty).
Best Answer
It is not only sane, it is safer than any other packaging you can make.
At least here in Germany, meat from the supermarket is not just wrapped in celophane, the celophane is glued to the tray. The packaging is air-proof. And the air inside the packaging is not normal air, it is a mostly sterile atmosphere with a composition different from normal air, which hampers bacterial growth (I think it has lowered oxygen content, but I'm not absolutely sure on that detail). This means that 1. no bacterial contamination is possible after the meat has left the packaging plant, and 2. the bacteria already present in the meat when it was packed grow slower than normal. So if this is your type of package, do yourself a favor and leave the meat in it.
I haven't frozen such packages, so I don't know how big a problem they have with freezer burn. But it may become a problem in the long term, as the moisture from the meat will sublimate on the inside of the celophane.
If this is not the type of package you get, and you have just plain clingy film wrapped around meat and a styrofoam tray (I've seen other products wrapped this way, but not meat), there is still no problem to freeze in it. The pad full of meat juices (this is not blood btw) is a good feeding place for bacteria, but the meat itself is as least as good as the pad, so you won't be reducing the risk if you remove it. By leaving the meat in the original package, you reduce the risk of additional bacterial contamination during transfer. And no other container will offer better food safety.
You can still consider a transfer for reasons other than food safety. First, you can portion and/or preshape the ground meat before freezing, and then you'll have to repackage it. Second, if the package is not tight enough, you risk freezer burn. But if these don't apply, it is probably best to leave it in the original container - this is convenient, and not dangerous at all .