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."
In these days of email and instant messaging, letter writing is becoming a lost art, and especially the formal letter. I’m pretty sure that formal letter rules are still taught in schools, but very little of it sticks. If you’re an executive or other high_ranking person within an organization, you can probably rely on your secretary or assistant to handle the niceties of letter writing, but for everyone else, knowing how to write a strong letter ourselves is important.