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.
Remember, you're hoping the person who receives your letter has no memory of your closing at all. The last thing you want is a hiring manager going into an HR meeting with your cover letter in hand, asking the team if they want to meet with "Mr. Kindest Personal Regards."