You're only looking at it from the shipper's perspective, not the receiver's. The postman is a romantic figure because of the recipient, not the sender.
And, frankly, the idea that my letter excludes your letter from the carrier's mailbag is laughable. No, they cannot fit in the same physical space, but there's room for more than one letter in the bag/carrier/truck.
Carrying letters is rivalrous. As more people send letters, the bag will fill up and more mail carriers will be needed.
Compare this to a real public good, e.g. national defense. National defense is non-rivalrous because me enjoying living in a non-communist country does not hinder you enjoying the same thing.
As for the postman being a romantic figure, not sure how that fits into the question of whether mail delivery is a public good or not.
And, frankly, the idea that my letter excludes your letter from the carrier's mailbag is laughable. No, they cannot fit in the same physical space, but there's room for more than one letter in the bag/carrier/truck.