NASA research brought us a lot of things in the past. Not so much any more. We get excited now about putting a camera with a transmitter out at absurd distances, to find out things about our solar system that will (possibly) affect our lives 50-100 years from now.
Would it improve if we took some or all of the money spent on NASCAR and funneled it into NASA? Maybe a little... but would the result be more exploration, or simply more expensive exploration? Money's really the only thing that could be repurposed, because there is certainly a limit on how many people can participate in NASA.