Rabbotai,
Why was Rebbe worried about a problem with the yichus of Bavliyyim and his descent from Hillel? Everyone knew that Hillel comes from Bais Dovid Hamelech.
R. Yehuda Hanasi was from a family that had been in Eretz Yisrael for generations. There must have been several generations from Hillel who lived before the churban until Rebbe. Do you retain the term Bavli forever?
Was Hillel really a Bavli? Didn't he learn with Shemaya and Avtalyon in Israel, then go to Bavel and then return to Eretz Yisrael? Was he a Bavli before he learned with Shemaya and Avtalyon?
B'kavod,
Samuel Kosofsky
Hillel was famous for being from Bavel, as he lived there for the first forty years of his life. Moreover, the Seder Hadoros says that he talked in Aramaic, as evdienced by the different places (especially in Pirkei Avos) where he states things in Aramaic (very uncommon in the Mishna). The Gemara even calls him "Hillel ha'Bavli" (Pesachim 66a, Sukah 20a). Based on the Seder Hadoros, who says that "he came from Bavel at forty years, learned for forty years, and led Bnei Yisrael for forty years," it seems that he learned from Shemaya and Avtalyon in Eretz Yisrael, but did not go back to Bavel.
All the best,
Yaakov Montrose