It doesn't need to make clones into absolute copies of them to be problematic. It's just an obfuscation of a very old idea, the divine right of kings.

It could be argued they would likely be worse than the original. They would be even more detached from the rest of humanity because of their position. They wouldn't be just a person that found an extreme level of success, they would be the undying legacy of that person. This is not a way to build a healthy human psyche.