Shanghai - (caveat you might see this elsewhere however remains true)
It's a victim of the battle of internal politics between regional and central government agencies.
Shanghai is not an Air China preferred airport however they do serve A* partners hubs in Germany with Milan and Paris added as premium heavy destinations within Europe. They only fly to Beijing from Heathrow.
The regional government sponsor China Eastern and they aim is to get slots in Beijing to start Long haul services from there.
The central government and through their agent CAAC continue to block this so the regional government in turn block Air China expansions in Shanghai (won’t give them slots)
As said countless times nothing in China is as it seems or as easy as simple market forces. Aviation is no different and long haul in particular remains a serious tool for the political power and projection aims and goals of the Communist Party over simple market forces, indeed some of those goals conflict between regional and central government agencies.
In basic terms the state through the CAAC remains all powerful and a multitude of differing and sometimes colourful liveries can be something of an illusion.
Air China can do no wrong - are the preferred carrier for All premium heavy long haul routes from Beijing and indeed major regional cities particularly Shanghai and especially those to *A hubs.
China Eastern get what they are given from Shanghai mainly to partner alliance hubs - in the main Skyteam and a few premium routes such as Shanghai To Heathrow
China Southern are also a regional player from Guangzhou with similar flights to partner alliance hubs and Heathrow - Interestingly through they do have traffic rights and operate to Amsterdam from Beijing -The only big three European route from the Capital and not in the hands of Air China.
This is something of an historical anomaly as they were originally awarded the routing Guangzhou-Beijing-Amsterdam with the stop over mainly due to performance issues at the old Hongqiao Airport some years ago
Then you have Hainan Group they are the tool for many secondary markets and none Hub to hub routes in the main.
Beyond that a few other regionals have been granted long haul from smaller Chinese cities for which Air China and the other two big grouping have little interest.