It can cause realism issues. For example, if your soldier was shot in the back -- you would presume him to be a Yoga master to be able to patch that?
Full explanation here
http://www.writerlot.net/gary0064.htm - along with a statement that medkits are designed to be used on one's self
There would be more than morphine and band aids in a sci-fi medical kit, no?
Assuming it was doable to have medkits less effective when used on self, I don't see any game balance or realism issues with this. Self-medication should be a last resort, when a soldier has 6hp and 7 bleeding wounds and nothing else could prevent death, it should not replace current use model of medkits.
I'm rooting for this idea because it does a disservice to playing experience when a soldier carrying a medkit dies of wounds during the same round he was injured or the very next round; current wound system is great with that exception. There should be time to try and save the wounded soldier, isn't that the whole point of it? The guy still runs as fast as ever, operates complicated alien equipment like nothing but can't try and to compress his own wounds to reduce bleeding, c'mon.