It also starts the clock for your boss and your company, kicking off the transition plan of training, hiring, and otherwise covering your impending departure. The bad examples here are all too vague. With the last one, you're aligning yourself with company policy, which is good, but it still doesn't tell the reader how much notice that actually is. Be as specific as possible on the time you have between now and your last day.
Why a Resignation Letter? In these digital times, why should we submit a resignation letter, anyway? A paper trail does seem old_fashioned, but in this case, it's a best practice. It makes your intentions clear, as well as the conditions. You're removing any ambiguity about the end of your time there.