The iPhone was released when I was in high school and before buying one it was very stressful knowing there might be emails I really need to respond to asap, but I can't even know if they exist.
With physical mail it didn't matter since there were big delays and no expectations of fast responses.
I don't think the phone is the issue, but the bad habit of signing up for services that will give you notifications the importance of which is impossible to tell until you've checked (is this a like on a photo or an important message from a relative?)