Much of the time being direct and to the point in your writing is the best course of action. In these awkward situations the indirect approach may be better. What are these iffy situations? Perhaps you are writing to inform a customer they will not be approved for a credit card, or that their refund request is being rejected. These situations may not always deal with delivering bad news. Sometimes you just don't want to come off arrogant. Through explaining your reasoning for the main purpose of the letter, it helps soften the blow; and in many cases the indirect approach can help educate the reader.
I would argue that both methods, direct and indirect, are still very relevant today. In fact, many businesspeople combine the methods to get just the right tone for their letter. "They [businesspeople] reveal their conclusions and recommendations as they go along, rather than putting them first or last." Whether you use the indirect or direct approach depends entirely on the situation at hand. Each is useful in its own right.