Grilling hot and uncovered helps to get that nice seared crust on the outside while keeping your meat nice and pink inside. It also helps to start with a cool dry steak. Oil and lipids are great, but if there is water or water based marinade in the meat, this can steam the inside and take some of that pinkness away if you like rare meat. The fat will make your steak juicy anyway.
When the lid is closed your using a combination of grilling and baking which cooks the inside more too. That's not a bad idea if you like your meat med well or well done and you want your meat cooked all the way through. That's definitely not a bad idea for chicken but it doesn't sound like the way you like your steaks.
That being said, I have to call attention to a great idea Steven mentions in How To Grill p. 127. (How To Brine and Grill Pork Chops) In this recipe, the pork chops are first smoked in the grill for about 20 minutes before being moved directly over the heat. If you are smoking with a low temperature and your starting with a cool or even a cold steak or chop, this is a great way to get some extra smokey flavor and still keep all the advantages of cooking over high uncovered heat.
If it aint broke, Break it!
Then rebuild it better.