Korach ben Yitzhar ben Kehas ben Levi - but not ben Ya'akov

Korach ben Yitzhar ben Kehas ben Levi…
Asks Rashi: why stop at Levi and not trace Korach’s yichus right up to Ya’akov Avinu? The Midrash answers that Ya’akov foresaw the rebellion of Korach and davened that his name not be associated with an evildoer.
The Questions: (1) Even if Ya’akov’s name is not mentioned, we all know that he is the great-great-grandfather of Korach, so what is the gained by the omission? (2) The implication of the Rashi is that had Ya’akov not davened, his name would have been recorded as part of the yichus. If there is a negative connotation to being mentioned in the yichus of a rasha, then even without his tefila, why should Ya’akov be mentioned? (3) And if there is a negative connotation, why does the Torah name Yitzhar, Kehas, and even Levi?
The Radomsker’s approach here is a delight (if you want to see it inside, it’s not on Korach, but on P’ Nitzavim, in the middle of the Rosh haShana derasha). He quotes the SHL”AH haKadosh who explains that the pasuk “v’zacharti es brisi Ya’akov v’af es brisi Yitzchak v’af es brisi Avraham’ is part of the tochacha itself and not a consolation. Davka because we are a ‘ben tovim’, a descendent of such fine forefathers who were role models of avodas Hashem, are we that much more culpable for failing to live up to their example. Here too, the Torah records Korach’s yichus not simply to identify him by lineage, but to reinforce his culpability. This was not some ordinary guy starting a rebellion, but this is “ben Yitzhar ben Kehas ben Levi”, a person who had such illustrious role models, yet who failed to absorb their teachings. Rashi’s question – if the Torah comes to condemn Korach as a rasha for failing despite such great yichus, why not put the final nail in the coffin and trace his lineage even back to Ya’akov Avinu!? To which the Midrash answers, although Ya’akov foresaw the evil of Korach, he davened that his name should not be used as a tool to prosecute even such a rasha.
(I have a neighbor who bought a Tiferes Shlomo because he knows I love it and my chavrusa has learned it as well; he read one mystical piece and threw in the towel. The key is to start with the pieces like this one!)