When I was on beta blockers for my blood pressure, it was the worst time of my life. Not only did I not suffer any nerves, but I couldn't experience ANY emotion; it was like I was a zombie. Not feeling nerves is one thing, but I never felt disappointment or despair, and worse than anything - I never felt joy or elation at winning. There was no adrenalin rush, no relief, no nothing. It also prevented me from "digging deep" when I was in a pressure situation, which is very counter-productive.
Beta blockers may be good as far as your health, but they can destroy all emotion, and anyone in competitive sport can tell you that emotion is the biggest "hook".