I prefer burgers that are made with blends of premium cuts of beef. These cuts (from the back half of the cow) tend to be flavorful even when completely raw. Skirt, Rib, Sirloin, Round, etc. Burgers made from higher quality, flavorful cuts should be cooked Med-Rare, so that the quality of the ingredients shines through.
When ordering a burger made from ground Chuck, it is best to request that burger to be cooked to Med-Well or, at least Medium. Here's why....
The primal Chuck is from the cow's shoulder; it accounts for approximately 28% of carcass weight. It contains a portion of the backbone, five rib bones, and portions of the blade and arm bones. Because the cow constantly uses its shoulder muscles, Chuck contains a high percentage of connective tissue and is quite tough. This tough cut of beef, however, is one of the most flavorful when properly cooked. The cooking process melts the collagen prevalent in the Chuck. It is the collagen that gives Chuck that distinct beefy flavor, which would otherwise be missing.
The temperature at which beef collagen melts is about 68 degrees Celsius (154 degrees Fahrenheit). The temp for Med Rare beef is between 55C and 60C. As you can see that's just not a high enough to melt beef collagen. To get to 68C, the beef must be cooked to an average Med-Well. Now, to get a burger even to Medium, you generally get the outside to Well-Done. That will melt the collagen in the outer portion and still leave you with some blood.
The mechanical action of grinding aids to speed even heating throughout the burger patty. Additionally, the cooking process continues off of the cooking surface so that the small amount of collagen in a hamburger patty has ample time to melt. To further ensure that the collagen melts enough to provide a good flavor, I tend to allow my burgers to rest for a few moments prior to eating them.
One can eat Chuck at a far lower temp, but the un-melted collagen will not provide additional flavors. We've all had plenty of bland Chuck burgers.