The erasing or dampening of your memory does change who you are as a person. I am who I am today due to my memories. My memories have built me, weakened me, and made me stronger. Without the memories that I have, whether they are good or bad memories, have made me who I am today and have shaped my personality overall.
Life experiences and memories make humans who we are. Without past knowledge, how are we to rectify our own experiences and learn from our mistakes? The human mind already represses memories for situations that are too painful to remember. We don't need drugs to destroy our memories as well unless someone's life is directly threatened by those memories. Other forms of therapy should be tried first and propranol should be used only as a last resort.