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.

That's advertising with extra steps. Apple having created an ingroup and an outgroup is very effective advertising on their side.