If the analogy is accurate, then the pre-addressed envelope that comes with your bill already has the unique address on it, so you don't have to do anything special. What's the problem?
Ah, good point. I said electric bill, but was mentally focusing on the few checks I still hand address, for which I don't necessarily receive monthly bills (rent, etc.).
For that scenario, you'd presumably have some system worked out where you can quickly say, "hey, what's the address for this payment?" And being on the internet instead of going through the mail, you don't have to wait a week for the answer.