It would "level the playing field" but it wouldn't promote true equality. People who want equality would protest the biased system, not the attractive people themselves. You don't hear many rational people saying they're anti straight people or anti white people. They're anti-homophobia and anti-racism.
Uh... because there are no two people in this world who agree on what is attractive, and there is no conventional standard of beauty. It's in the eye of the beholder and varies from person to person. How would you even devise a scale to measure it, and on what criteria? There are none that are universal.
Who said everyone wants equality, let alone equality in every aspect of their lives?
Lookism is a real thing, and it should be legal to sue for discrimination against unattractive people. However, the disparity in income between an average highly attractive person and an average ugly person is far less than that between of the lower class and the top 1%, which I assume you're alluding to.