I would say "nationalist ego" instead of military advantages. Edmund didn't bring back any new weapons from the Pole. And, for that matter, our 1960s-70s race was as much (or more) about oneupmanship than gaining real tactical advantage - although of course a lot of the experience gained supported ICBM development.
This is an unfortunate reality of our society. We've only ever spent dollars in space when it was advantageous to our Department of Defense, and the military in general.
People and companies who have succeeded in space have tied their goals to overarching military objectives. It's the best way to win the space race. Make the military understand they need to do the thing you want to do.