But would NASA out-perform a research university with the same budget, tasked with addressing the aforementioned problem/solutions directly rather than incidentally?
Yes. NASA is drastically different from an academic institution and the difference in administrative culture alone allows it to be a more effective multidisciplinary research organization working on everything from pure science to industrial ready technologies. For example, Black and Decker developed the first cordless vacuum after their engineers got an idea while working on cordless drills with NASA in the same research center where they were working on Apollo 11+ and photovoltaics. Universities are simply not made for this purpose, since they focus on basic research and education.
Furthermore, much of NASA's success is due to the mix of scientists from different fields, universities, and business working on one problem. When the best of the best come together, it results in a cross polinatiom of ideas. It's not just being in the same building or sharing a cafeteria while working on disparate grants, but a day to day sharing of knowledge to tackle a single problem.
This is a really well-informed comment and I wanted to say something else in support of it.
A Caltech scientist who had worked with DOE and NASA labs made an offhand comment about the kind of work that those labs are suited to do that stuck with me - he said they should be trying to solve problems that are "national lab hard" - kind of a play on NP-hard.
What he meant is that these environments are suited to solving complex cross-discipline engineering/science problems ("make the right measurements to understand the climate system", or "find the processes and materials to make air travel safer", or "put a huge infrared telescope in space").
These are not problems that are suited to a university research structure. They don't get solved with $300K/year grants, small collections of discipline-focused PIs, and transient grad students.
Think of how many prerequisite advancements are needed for deploying GPS. Now task a team with developing only GPS but not anything that might enable safer launches or better solar cells in space. They eventually develop a GPS solution but in order for it to be as good as what we got they would need to be part of a group full of interdisciplinary teams that would look allot like NASA.
Or if you prefer a programming analogy, what if all software teams only built what they were explicitly tasked for and could not collaborate on the tools used. Managers _might_ get their deliverables faster but I suspect by not developing tools incidentally we leave out future productivity gains.