As discussed by Brandon, not only would a civilization dominated by appearances be impractical, but it also would not make sense as appearances are generally a subjective view.
If we were to look into the success stories of today's most powerful people, we may find some which were influenced by good looks, however most will be dominated by a great mind. The reason for this is that the only real role that attractive people play in the world (assuming their appearance has to do with their success) is to act as a front for the ones with great minds. There will always be a demand for people with great minds as they are the people who actually help mankind progress. However, there are no roles which good looking people can fill which actually benefit us in some way. It is true that technically some people can have a successful career based on aesthetic appearances, but if everyone who was attractive relied on this, they would most likely live in misery after realizing there is in fact someone who looks better.
Looks are simply not as complex as a great mind. For example, if you were a model and your modeling agency went out of business, you would have no choice but to take any job you can find. But if you were a medical practitioner or anything else requiring a good mind, you would have much less trouble finding new jobs as your skills are actually in demand.
One of the only exceptions to being a model or an actor/actress is combining good looks, promiscuous activity and a normal office job. This may be getting further in life by the definition of some people, but this would only last for the brief time between 20 to about 40 years old, at which time their looks will deteriorate. You could say that a great mind may be crippled by Alzheimer’s or schizophrenia, but this is simply not a logical argument as there is a 100% chance of both the standard of good looks and good looks itself to fluctuate whilst the mental state of a person normally remains consistent.
Bill Gates is a good example of how a great mind (business and mathematical) can get you much further than good looks. He is one of the richest people in the world, mainly due to the creation of the VisualBASIC programming language and the sale of the Windows operating system. He acquired this success through genius, and sometimes controversial, promotional techniques as well as his knowledge of personal computers. At no point were his good looks involved in this process.
One obvious example of where a mind would do more than looks is in a test, such as the selective schools test. At no point is a photographic ID required for the completion of this test, and your appearance therefore would not provide and bias. The only thing next to your name and your mark is a student ID, not a photo. I don’t find numbers attractive, do you?
According to the list of billionaires in 2007 as published by the Forbes magazine, not one of the 100 richest people in the world achieved this level of wealth by pursuing a career in acting or modeling. The logical and statistical evidence is overwhelming; and clearly demonstrates that <case line>.