It's a common attack on public goods: Amtrak & USPS, but would never be asked of the Military or FEMA.
Amtrak and USPS both charge for services. It's reasonable to expect them to not hemorrhage billions of dollars annually as well.
Further, it can be argued a private business could operate on USPS or Amtrak scale with greater efficiency, cost much much less, and even turn a profit (see SpaceX).
Some parts of the military charge consumers, don’t they? For example, military Exchange stores charge for goods, but are also partly subsidized by direct appropriations - and the “profits” go back into military quality-of-life programs. You could decide instead to forgo this charge since as you say the military is not designed to turn a profit, but then you’d have to deal with all the perverse allocation problems and incentives that might pop up if everything in the store was suddenly “free”. Adding a cost to items helps to allocate limited supply (and helps to defray costs to the taxpayer of other military programs), even if the military as an overall organization is intended to direct taxpayer funds into achieving a purpose.
Now take that same idea and apply it to “providing government funded public transportation to make a city economically viable”, or “maintain a constitutionally mandated postal service”. Taking money for services is not incompatible with being fundamentally a government-funded service that expends more taxpayer funds than it brings in.
2. SpaceX, one could argue, is being subsidized majorly by the US government, for strategic reasons. I'm pretty sure it would have gone bankrupt without government intervention.
3. Almost no passenger rail system is fully profitable, in the world. Just like education, it's something you still want because it's a community/public service.
The assertion was a privately run company could do what USPS does a lot better, for less cost, and likely provide a better end result. SpaceX is an example of that, but there are many others.