As Batman, Bruce takes a serious whoopin' regularly enough. In some canons his cowl probably offers some protection but as any UFC fighter's face will tell you, a career in fist fights will inevitably cause you some disfiguring injuries.
Do we ever see Bruce getting re-constructive surgery to keep his handsome face handsome? I feel like Batman wouldn't care how he looked, but Bruce is expected to.
I'm talking about purely cosmetic surgery here.
Possibly related: How does Bruce Wayne mask Batman's injuries between beatings?, but this question makes no mention of Bruce possibly going under the knife to repair any facial injuries.