As far as raising rates, that may or may not work out, it any event, it would be a short term solution. As soon as they get more revenue, they’ll just spend more. If you’re starving to death on $20K a year you’re going to starve to death on $50K.
Anyway, I would guess that bulk mail is the easy money, it goes to every mailbox on the route. You get two “real” pieces of mail a month that the USPS grosses $0.88 on, and get 100 pieces of junk mail a month that the USPS grosses $22.00 on. The mailman walks by your house every day and the infrastructure has to be maintained either way.
Were I going to compete with the USPS, I’d go after the junk first, let the USPS worry about sorting out all the birthday cards with kids scribbling grandma’s name and address on the envelope.