I don't have paperless billing, but I do have email notifications for when my bill is ready and due. I actually recently had to update my profile under My Verizon account online with my email address as somehow it switched to sending those notifications as a text message and I know I hadn't changed it to text messages.
Why you don't have the same access is strange. Are you signed into your MyVerizon account as the account owner? That's the only way I can think you might not have access to make those changes.
If you have tried all of ways to access your profile in your MyVerizon account online and can't change it, perhaps you could call customer service at 1-800-922-0204 from a landline or *611 from your phone and ask the representative to add your email address to your account.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.