I use a baster and have never had a problem with the top part getting too hot, perhaps you could consider getting a bigger one so that the fat doesn't get near the top?
Another option to consider is putting a lid on the pan and tilting it, over a suitable receptacle, then cracking the lid open slightly to allow the fat to drain out without releasing any of the meat.
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.)
Best Answer
This is partly down to taste. When you make burgers much of the fat runs out by the time it's done, so you need to start with a high enough fat content that the burger isn't dry when it's done. I've made burgers with 10% fat when that's all I can find rather than 20% (my personal ideal), and they are very tasty as long as you don't overcook them. I find the extreme of 30% which I've seen recommended in places to be too greasy, but again that's my taste - I find too much fat covers the flavor of the meat.
Where you have to be very conscious of fat, whether minced or not, is in dishes where the fat has nowhere to go, like stews, braises and casseroles. Very fatty meat in these can end up with a greasy end result, which is not to most tastes. I use around 10% mince and lean cuts for those types of dishes.