It's a shame Kana didn't hear the most important part, which Archer left for last. She's free. The Magics of her Brother and her Mother are bound to the legacy of the Tokhsaka crest, and therefore cannot be freely defined. But because a Sword has no inherent meaning, she is free to construct whatever meaning her heart desires to the Sword that is herself. She's free and Ritsuka is a slave to the Tohsaka Crest, since I don't think Ritsuka's sense of responsibility allows him to decline eventually inheriting and building on top of the crest inherited from his mother (which is why Gilgamesh suplexes him, because this sense of responsibility probably makes Ritsuka as boring as Tokiomi from his majesty's viewpoint.)
She, on the other hand, has to build her magic from foundations up, but it also means that she isn't obligated to build on the foundations of her father, and she really shouldn't because she must define her own meaning, because she is not Shirou/Archer and should not ever be Shirou/Archer. So starting again from the fundamentals is necessary because it gives her the building blocks to define herself. Honestly, I think GIlgamesh is disappointed in her: why would someone of that kind of liberty sacrifice it to imitate a Faker? She is clearly a superior Sword to the Faker of her Father - Damascus Steel to a Copper Knife. Kana has more freedom than just about any other daughter born to a Magus in her own time-line, why forsake that freedom? There is probably any number of children born to Magi her age that would utterly envy Kana's liberty.