I hear USPS worked phenomenally well until it became a political target. I think the issue is less that we can’t and more that we won’t support or improve these systems for ideological reasons.
It's like saying AT&T "worked". Sure you could buy a phone service and pay $$$$ for it, but if I had a better way of running it, they would put me in jail for trying.
The monopoly is only over mail and is scarcely enforced nowadays. And yet USPS is still cheaper and better on parcels where it doesn't have a monopoly, so much so that private parcel delivery will often just use USPS.