We put every billing service we can on paperless!
We have such unreliable postal service here, and we live near a town with 4 million people in it.
We routinely have new postal delivery folks and some appear to be less than quality conscious. We just went for 4 days with no mail (the whole street). Come to find out after going to the post office since they won't answer the phone, our "normal" delivery person was re-assigned and no one really did much about re-establishing service.
In the last year I have had envelopes with Amazon gift cards not show up, have gotten someone else's mail order prescription, had a new cell phone disappear, have had packages show "delivered" on the internet tracking and not show up for several days after, and on and on. Our neighbors are suffering the same lack of service.
So, if they want to steal or mis-deliver my remaining junk mail, have at it!
Anything new I buy from an internet vendor, I specify UPS or FedEx where I can and pay the extra freight.