I recall there was some understanding that it had a legitimate use as well as the obvious marketing, which was to advise the reader that the message may be unexpectedly concise or contain errors because it was sent from a cell phone, something less common before the iPhone came out. BlackBerry phones did this too for the same reasons.
You misunderstand the purpose of "Sent from my iPhone" - it was a status symbol, it showed that the sender was part of the superior iPhone owning elite. It was trivial to remove, but most didnt "oh, I am too busy too remove it, I guess I'll just leave it and let everybody know I can afford an iPhone".
You are right, it was advertising, but it advertized the user, not Apple.
I always thought this was an implicit request to forgive obvious typos and autocorrect mistakes. Sent from a mobile device (iPhone, Samsung Galaxy, Blackberry, Windows Phone, etc.) with a tiny keyboard and in a setting in which proofreading may not be as rigorous as normal.
“Sent from my iPhone” is a default signature, but you can change the message under Settings -> Apps -> Mail -> Signature (at the bottom of the options page)