Tl;dr: NASA was only incidentally about science, it was cover for funding military/geopolitical goals. Once those goals (moon, shuttle) were achieved, NASA's risks and costs are exceedingly hard to justify.
What NASA does accomplish is economic growth of America as a whole. What most people don't realize is very dollar given to NASA roughly translates to 2-4 dollars of GDP growth of American research, development, and manufacturing.
Really one of the most direct ways of the US Government putting additional money in the hands of the American is NASA's budget strangely.
On a person by person level yes there is likely some wasted talent at NASA, and their skills could be put to better use else where. But doing a micro-economic analysis of every 1 person's case over 300,000 employes and 18,000 contractors would be very time consuming then making boarder macro economic statements. Also remember micro-economics are wrong about certain things, macro-economics are wrong about things in general.
Assuming you're talking about the '60's, it's the other way around. If you're talking about today, it's still the other way around but the number of contractors is much smaller.
(Aaahhhhhh! Cognos! Aaahhhhhhh!)
I don't have a good source for the number of contractors, other than wikipedia. (...which cites http://employeeorientation.nasa.gov/contractors/default.htm. Huh.)
Aha! Now we know where NASA's IT budget went -- to IBM.
IBM specializes in making sure that you spend your full IT budget each year, so that upper management isn't tempted to cut it next year.