It is established etiquette by the Joint Chiefs of Staff, United States Department of Defense, the U.S. Army, the U.S. Navy, and the U.S. Air Force that the closing “Respectfully yours” be reserved for the President of the United States (according to U.S. Army standards, this also extends to the first lady and the President_elect).
Consider the daily life of whomever you’re sending a letter to _how many other things might they have on their mind when they read your letter. Maybe they have a meeting in five minutes. Maybe yours is one of 200 letters they have to wade through. Maybe it’s the end of the day and they’re worn out. Giving them a concrete action to take makes it all the more likely that it will “stick” _ they’ll add it to their todo list or their calendar, they’ll pick up the phone, they’ll check out your website, or they’ll respond.