Weiss got her face cut open and it didn't seal like Jaune's cut did and she's a more experienced aura user. I'm thinking the cut thing was just thrown in for flavor. I'm of the thought process that semblances aren't just a specialization of your aura, but a unique ability.

Still, if everybody can become wolverine and everyone is a field medic, it'll make being wounded just something to shrug off. Oh, you sliced my torso open? I can heal that. I'm low on aura? I have three other teammates who can do it for me.