So are people happy to receive bills by email? (Ok, Telecom has MyTelecom, but a lot of orgs just email bills) What come back do you have if the email doesn't arrive? I've never had a posted invoice go missing but emails regularly go AWOL. And there is legislated privacy over post, but not email.
I personally get emailed bills from the power company, Snap, Sky and 2Talk. In the 4 years living at my current address (when I signed up for all these accounts) I have never once missed a bill from them. They always get through. Emails go 'AWOL' when people accidentally hit delete or have poor junk mail controls.
Use a good email provider and good automatic sorting controls and you will never miss an email.