As a Brit I'm a bit skeptical about anything below a well done burger. We were taught that you should always fully cook ground beef as the mincing process can mix in pathogens from the surface of the meat. I suppose this doesn't apply if the beef is safe to make tartar with or maybe if you sear the outside of the cut you're going to mince before mincing it.

That said a number of mid-range burger chains offer rare burgers here, and in such cases I tend to go medium which typically nets results on the less overcooked end of well done anyway.

They might like the taste of caramelised meat.

I also like my steak well done although we also eat sushi and proschutto.

I would never eat a not fully cooked ground beef product from a random burger store. That's just common sense, ask your mother.

Any reason why? Someone else mentioned they also murder their steaks...

Might as well not even eat meat if you're going to incinerate it.