I don't think factionalism is as strong as it used to be, especially during the Jiang Zemin and Hu Jintao days. All the factions have been practically stomped once Xi came to power, or at the very least Jiang's clique as well as the Princelings have seemingly lost influence on Party affairs. My take is that Li Keqiang keeping his job in the 19th Party Congress indicated that Xi didn't have the political clout at the time to completely stymie Hu Jintao and the Communist Youth League faction. However based on my understanding, the presence and influence of the CYL faction has "eroded" to a symbolic one over the course of the 19th Party Congress. I would put down the numerous articles the past year or so linking Hu Chunhua to scandal as Xi's own faction pulling strings behind the scenes to ensure that Hu, who will become the de facto number 1 figure representing the CYL faction if Li steps down from the Standing Committee, could potentially be vulnerable if he doesn't tow Xi's line. In essence a proverbial gun is being waved to his head to make sure he behaves. Keeping Hu could project an image of unity to the public amongst the party despite factional differences, as ousting him could get very ugly given his "young" age and remaining eligibility to stay in elite politics. That's just my gut feeling.
I wouldn't exactly say Hu, who manages agriculture and rural affairs, has a bigger portfolio than Sun Chunlan, who manages health care and education... I'd even say Sun has had the spotlight shun on her throughout the pandemic as well as during the private tutoring crackdown. I'm just saying Hu's portfolio isn't as "sexy" or as "important" as finance and trade. I might've worded it poorly, but what I was trying to get at is that titles and rankings in the State Council (Premier, Vice Premier, State Councillor, Minister etc) are almost meaningless under Xi, so it doesn't really matter who gets named Premier. Food for thought the current Minister of Public Safety (supposed to report to the Political and Legal Affairs Commission) as well as the Minister of Commerce (supposedly under Hu Chunhua's portfolio) seemingly share Politburo status, as they almost "subvert" or "supersede" the parent Party/State Council organ that is supposed to govern them.
As for Chen, he'd only have one more promotion in him after the 20th Party Congress if the usual age rules were to be abided. That's why I have him as an "emergency" or short term successor should for whatever reason (I'm thinking health or age) Xi has to step down during the 20th Congress. I don't think he has developed Xi's type of political clout to subvert Politburo age rules in order to be a long term successor, he'd be at most a one-and-a-half term General Secretary.
And Xi can become the Chairman of the Party if he cares about the titles, as 
