Always appreciate 高新‘s (author of 夜话中南海) insights on intricate personnel issues. But in Cai Qi's defense, XJP's own ascent to the GPS is nothing short of air-lifting.
https://twitter.com/You_Shu_China/status/1329622803973238787

He was not a Politburo member when he was appointed to Shanghai as Party-Secretary, a position customarily preserved only to a Politburo member. After serving merely 6 months at that position, he was
lifted directly to Politburo SC, skipping the crucial rank of Politburo.


But then, Hu Jintao had also skipped the Politburo and was directly promoted to its standing committee. So, the rank seniority rule seems to apply less when the office concerned goes higher up.

We cannot call what had transpired as the promotional path of the General Party-Secretary in merely 2 cases as a pattern. But if I have to venture a guess about who the next Party leader will be, I would look below/outside of the Politburo.
