- The private company can do the task more cheaply than the government and
- The private company can still make a profit and
- The quality of the task doesn’t suffer too much.
If (1) isn’t true than there’s no point in having the function privatized in the first place. If (2) isn’t true than no private company will want to do it. And even if (1) and (2) are both true but (3) is not true, then tax payers would still prefer have the government provide the service.
In general, I think it’s unlikely, for most government functions in the U.S. economy to satisfy all three. The USPS may be one that does so long, as Yglesias says, the market is competitive. Basically, all you would have to do would be to allow other firms to deliver to the mailbox. The only question is whether some rural communities would completely lose service.