How about in order to do the running vault, the weapon must be lowered? This way the character has a free hand to put onto the obstacle and use whilst vaulting it. Ofcourse only when running, to allow the momentum to carry them over the obstacle. It would be great for getting over them mid-sized obstacles. If there is no obstacle near the player the function could not work, to avoid people exploiting this or killing the realism/immersion on an open field say.
Also, I'm not sure if anyone has tried climbing rocks on Stratis, but I'd also like to see some sort of step up option implemented, even if it only worked on rocky areas. Perhaps similar to above but when stood still or walking. So again, you'd need a hand free (weapon lowered) and then you could step up onto the obstacle (providing it is no higher than waist height).
EDIT: I voted yes to running vaults but only if it was something like my suggestion above. I don't want Parkour in combat gear to be implemented.