I have one American Express card that I was still receiving paper statements for as I have been too lazy to go online and switch to online-only statements. That turned out to be a good thing as an insert in the latest statement that arrived in my mailbox had an offer to switch to Online-Only statements. I completed the offer the other day and will await it to be credited to my account within 90 days. The offer runs until November 30th so if you haven’t seen it in your postal mail yet there is a good chance you will in the next few weeks.
You can access the offer here however the T&C’s do make it seem like it is a targeted offer:
The same account associated with the Basic
American Express Cardmember that has been sent this offer must enrol in
Online-Only Statements to be eligible for this offer.
Still, it may not hurt to give it a try if you never received the insert with your paper statement. Of course if you are already receiving online only statements you are out of luck as well.