Well it could be annoying or could it also be flattering to the recipient? Let’s look at it both ways.
‘Sent from my iPhone/Blackberry/Android’ signatures are inbuilt with an insinuatory apology and snobbishness that can be construed as “I know there might be typos which I’ve overlooked, I might be replying in mono-syllables but hey cut me some slack! I’m typing this on miniscule 5mm keys with my thumb of 25 mm sq. surface area so that I can be done with replying to your message/mail before I get drowned in a sea of other e-mails”
Or it could also mean “Your mail is very important to me and I don’t ever want to keep you waiting so I shall reply to your mail, typos or no typos, even on the go. What is important is that you hear from me promptly and I will make sure that it happens regardless of the brevity of my message”.
I recently got an e-mail with the signature ‘Sent from my iPhone. I also own a Ferrari’. Agreed that ‘Sent from my…” could come off as being slightly ostentatious and there can be other variations such as ‘Sent from my mobile device’ or ‘Sent from my wireless’ etc. But it’s really about whether the glass is half full or half empty.