If your screen is so small that it can't display 80 characters across then pretty much anything you look at it with is going to look odd. Any HTML formatting such as tables will also be painful to read.
I just checked on my phone some random opened web page: with my settings (which are far from the default - I raise the DPI setting and the font size so I have small UI elements but big texts), it displays 45 characters per line on portrait mode. Actually the font size is a bit too high, but I don't really care as far as most web pages are readable. I'm fine with scrolling the occasional big HTML table, and will change the settings if this becomes annoying.
So, yes, sometimes, my screen displays less than 80 characters and is perfectly usable. And this fact is not really of my correspondent's business, whether they choose to manually wrap at 80 characters, 72 characters, 42 characters or some other arbitrary number of characters. Actually, nobody knows that apart from people who read this comment. I display text as I see fit (and this is totally an intended pun).
That said, wrapping is better left to the mail client, and let the user adjust their window to suit. My chief gripe at this point is that some email clients (gmail anyway) will get confused by outsized inline images and wrap on them, even if that means letting text drift off the side of the screen!