The journey to the moon was an example of this. Did we do it efficiently? Probably not. We spent tons of cash and resources that otherwise may have been used more efficiently, but we achieved the objective.
During war, the biggest gain is SPEED in the prioritization and removal of red tape, and acceptance of risk (death, health risk, etc) to achieve the objective (as you mention).
Want to build a nuclear reactor in Chicago? Go for it. Have to build TWO competing uranium generating plants to hedge your risks at the costs of billions? Yes, of course. I would hesitate to say, however, that war develops these innovations more efficiently than at other times.
Not just government. During WWII, removing roadblocks to industrial productivity was a focus of government-industrial joint effort. Now, creating such "moats" is a focus of effort and policy.
Or take science education. During the cold war, there was much concern that it actually work. Else we fall behind. That concern permitted disrupting existing interests. Now... not so much.
As the saying went, "The US Army is at war. The US is at the mall".
I would not argue that this was efficient, well organized, or toward a single goal, but rather got a bunch of money dumped on it due to national priorities and something shook out.
There were also steps backward in preparedness due to the focus on counterinsurgency ops, e.g. loss of experience in areas such as air defence and armoured warfare which weren't relevant for most of the operation (also in Afghanistan).
As someone from a country that lost 20% of it's population to it, I'm going to go ahead and say that the last thing I ever want to see is another war that poses an existential threat to a superpower surrounded by two oceans.
Innovation during war is expedited because while the government and public agencies are massively inefficient during peace time. In war the brightest resource are drawn/forced to align with the government, increasing its capability. Whatever redtape that used to exist are now ditched for more efficiency, while if you keep being a massively inefficient government, you risk losing the war and everything. All of these factors proceed to make innovation pace much faster on matters that are somewhat related to military.