The argument is that as companies waste more and more money; as they become more and more inefficient they become less profitable and less competitive. Over time, companies that become wasteful go out of business.
I generally see services/products without much innovation, huge barriers to entry and/or little change as candidates for being public services. Any kind of insurance is a good example. Government bureaucracies can be very efficient: consider private health care insurances vs. medicare.
In these scenarios private organizations often drive up cost/inefficiency, because they only way to introduce more profit is to drive up inefficiency.
Now, as governments and government agencies get more bureaucratic, more wasteful is there anything that stops this process?
Politicians... And yes, in other countries we do from time to time see massive reorganizations of public institutions.
I guess a crazy person could even argue that Trump is reorganizing or disorganizing a lot of US government agencies, hehe :)
As with software: it's all about picking the right tool for the problem at hand. I for one wouldn't want to see a government run clothing line attempting to deliver the latest fashion -- just to give a extreme counter example.
On topic: a for-profit investment might be what it takes to attract even more private capital. Especially, with the amounts of capital currently in play on the markets today. Granted I don't have the qualifications to know if there is enough basic research to foster hope of finding a cure.