"I think there would be a definite political incentive to have one, in that you could deploy soldiers without the media wetting themselves when they get hurt"
They have them already, they are called special forces.
The reason France was able to create and make such good use of the legion probably has to do with its legacy of multiculturalism and colonialism, but hey, PAX all the way, they wipe your record man, you can get away with anything.
http://en.wikipedia.org/wiki/Martha_Washington_(comics)