You're correct. The USPS provides a vital service not easily replicated by the private sector. However, if there were competition for first class mail (which indeed there should be) the USPS could and should be a much, much smaller entity. The savings would be in the billions. The USPS remnant would not be a profit making enterprise - in other words it would lose money - however, the losses would be a fraction of what they are now.
Yeah, but the idea behind making the postal service a monopoly is that the low cost deliveries subsidize the high cost ones, and it all works out in the end.
If you allow competition for first class mail, then companies will only deliver on the profitable routes, leaving the rural routes—money losers—to the USPS. That doesn’t work.
There are a lot more wastes of govt money to worry about than the post office, which actually provides low cost, reliable service to every person in the country.