I go back and forth on this, but tend to favor a reverse sear. I cook low with some smoke until internal temp hits 110°-115°. Then I let the steaks rest in a butter bath that includes garlic and fresh herbs while I get the grill temp up to 700° or so. Back on the grill for about 1 minute per side for a crisp sear, which is enhanced by the butter. Beats $50+ steakhouse steaks! However, if I’m in more of a hurry, I’ll cook as you describe. Reverse sear method can take up to an hour, but I’m retired, so I usually have the time.