Is it safe to overcook beef or other meat?
From a food safety point of view, no. There is no danger, because the meat contains no pathogens after overcooking. 

From a "healthy living" point of view, it might be a problem, because you can have created carcinogens by charring. But we don't discuss such topics here, because nobody in the world knows how much eating charred meat contributes to the risk of developing cancer. 

From a cook's point of view, you are doing it wrong. Well cooked meat is juicy and tasty. Overcooked meat is tough as shoe leather. You can continue doing it, if you want to, it is just irrational, like saying "I let my salad wilt for at least a week before eating it, I prefer it that way."