Tolkien doesn't say she's the greatest because she's the most beautiful, or because of her deeds. He gives no reason. He simply says she is the greatest of all the Eldar. I'll quote it one more time for you:
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Who together with the greatest of all the Eldar, Lúthien Tinúviel, daughter of Elu Thingol, are the chief matter of the legends and histories of the Elves.
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I hope you realize that you're not arguing with me, you're arguing with Tolkien himself.