Why was it Chizkiyahu is the one to come to be milaveh R Yochanan be Zakai
Shlomo Kravitz, Yerushalayim
1. The Shitah Mekubetzes (DH Amar) cites the Gemara in Chagigah (14b) which relates that a Bas Kol announced that Rebbi Yochanan ben Zakai, his Talmidim, and the Talmidim of his Talmidim were fit to enter the "Kas Shelishis" -- "the third group" -- in Gan Eden. There are seven "Kisos," groups, in Gan Eden. Chizkiyahu was also in the third group.
(When a person leaves this world, the members of his "group" in the upper world come to meet him.)
2. The Tzelach (the Noda b'Yehudah) gives a different explanation. He writes that although Rebbi Yochanan ben Zakai was the Nasi, he was not descended from David ha'Melech. This was in conflict with the rule that the Nasi should be descended from David, as Hillel and his offspring were. (The Tzelach cites the Gemara in Kesuvos (62b) that says that Rebbi Yehudah ha'Nasi was descended from Shefatyah ben Avital, who was the son of David ha'Melech.) The reason for this was that when Raban Shimon ben Gamliel was killed among the ten great sages murdered by the Romans, his son Raban Gamliel of Yavneh was too young to become the Nasi, so Rebbi Yochanan ben Zakai became Nasi instead. Therefore, Chizkiyah -- who was descended from David ha'Melech -- came to meet Rebbi Yochanan ben Zakai at his passing to show that Beis David held no objection against Rebbi Yochanan ben Zakai for having accepted the role of Nasi under these circumstances. Also included in this was a hint that the position of Nasi would now revert to the descendants of David ha'Melech, which is why he said "Prepare a chair for Chizkiyah" -- implying that the Nasi would now be from Chizkiyah's offspring.
3. The "Mesivta" printing of the Gemara cites Rav Sa'adyah Ga'on who, contrary to the Tzelach, writes that Rebbi Yochanan ben Zakai indeed was descended from Chizkiyah, and this is why Chizkiyah came to greet him. (A person's ancestors come to meet him when he leaves this world.)
(I have not yet been able to look up the words of Rav Sa'adyah Ga'on in the original source. This approach requires further elucidation.)
Kol Tuv,
Dovid Bloom