Not only does this mean that you should focus on neutrality in your letter’s appearance (avoiding the use of colorful paper, brash logo designs, and artistic fonts), but it also means that you should employ a very low_key, unnuanced, and professional closing phrase. The best_case scenario is that the hiring manager, colleague, or connection won't even notice the closing.
When you write a business document, you must assume that your audience has limited time in which to read it and is likely to skim. Your readers have an interest in what you say insofar as it affects their working world. They want to know the “bottom line”: the point you are making about a situation or problem and how they should respond.