As for private companies costing more to develop whatever, that should not be the case. I imagine that PSU's are very inefficient and very unresponsive. Non-government owned companies should be able to do what PSU's do much more efficiently at much lower cost. = high profit while still cheaper for GOI, doesn't it? The other aspect is that when problems are encountered, the more able management and more flexible workforce one would expect in a commercial company should sort things more quickly so delays would be less severe.
It is not about who is more efficient, but who gets what!
When you bring the private companies getting into the military industrial, the condition is that these private firms must have the knowledge, technician team, equipment and infrastructures to do the job. The tech standard of these in military industries are generally much higher than the demand of civilian industries, most of private companies don't need these. So, in order to make them capable of military R&D, they need to upgrade their existing R&D & manufacturing department so even build brand new ones. This require huge investment (billions) in a short period time. On the other hand, the military equipment development requires long period work, this investment won't see any return for decades, worst of worse the majority of these development projects will fail at the end. This is a high risk field for anyone. For western countries, their private firms have been in this business for hundreds of years, they already amortized their investment over hundred years. Even so, today, they still need heavily subsidies from their government even though they have the whole world as their market.
For those new players in other countries, even in the countries like Japan, Korea, they are all only private in the name. It is run by privately, but the countries provide fund, tech, and guarantee their profit. You could say they are all running at financial loss actually every year.