Here, this is the argument in favor of letterhead. I wrote a letter to a friend and the envelope got torn apart in transit. It was a regular old business envelope, plain white paper with blue patterned ink on the inside to make the letter hard to read, gotten in a box of 40 or 50 from any general store. Nothing remarkable or exceptional about this envelope, except that it happened to run afoul of a processing glitch and was shredded, its contents spilled.
By some lucky accident, I happened to have included my return address on one of the pages in this two-page letter. I don't recall whether I designed the formal letterhead described earlier in this blog or if I simply wrote my address up in the corner, but whichever, it was enough. The letter was returned to me by the post office in Madison, WI, with the pictured letter included. Usually I don't include my address in the letter itself, so I felt tremendous relief that this should have worked out so.
And yes, I realize most people don't write letters, they write e-mail if they write at all, and the concept of a return address is a thoughtless given. But, for those of us neo-Luddites who still know how to navigate a pen across a sheet of paper, I urge you to consider making up your own letterhead. It doesn't have to be fancy, nothing more than your name in 16pt. and address in 12pt., all in some interesting font (and gods knows there are many thousands to be had for free online). That would be enough.