I always thought that question got answered shortly after it came up: “You are right in thinking that he is under the British government. You would also be right in a sense if you said that occasionally he is the British government … They began by using him as a short-cut, a convenience; now he has made himself an essential. In that great brain of his everything is pigeon-holed and can be handed out in an instant. Again and again his word has decided the national policy.”
If we take Sherlock at his word, then the question isn’t really Why Does Mycroft Spend His Time Bringing Stuff To The Attention Of The British Empire? Instead, the question is, No, Seriously: Why Did Sherlock Spend The Better Part Of A Month Disguised As A Panhandler Of Chinese Ancestry To Investigate A Single Back-Alley Killing While His Brother Was Ably Solving Global-Ramifications Problems Involving The Royal Navy?