The problem is, government calls the shots and decides what is to be built. If they say "build a white elephant", the private sector will build the best white elephant money can buy.
The other problem is that, more and more, the government sets all kinds of conditions for contractors. They have to employ the correct percentage of women and minorities, they have to be sensitive to environmental correctness. And all of these things adversely affect safety.
FWIW, the work I have done with NASA, most of the line engineers are reasonably competent. Trouble is, they start up the ladder and become bean counters more than engineers. That happens in the private sector, too, but in the public sector you are further hobbled by bureaucracy and politics. Long-term planning becomes mostly a meaningless exercise when your timeline is a two-year horizon. Then again, the private sector can have much shorter time horizons, such as the next quarterly report.