Okay so thinking long term here. If Chinese private companies do succeed beyond our wildest dreams and completely upstage the government agencies, what will China do? For example, if a company manages to get something akin to the LM-9/Starship into orbit and landing by 2030, long before the LM-9 launches. Or if they come up with a a rocket rivaling the LM-10 and capable of reuse before the LM-10 gets into orbit. It's not impossible, if Space pioneer can get the TL-3 into orbit this year and land it by 2025, their development speed will make SpaceX look slow and the TL-3 will be the 2nd most powerful rocket in China.
Will they slow or abandon plans for the LM-9? Or just forge ahead with the LM-9 despite there being alternatives? Will they allow this private rocket companies to launch national prestige missions like the lunar missions?
This is an impossible proposition to begin with. These commercial companies will NOT make something (CZ-9,10) without state endorsement. Your question is asked in a reversed manner, it should have been "Is the government going to open up the launch catagory of CZ-9 and 10 to players other than CASC some time in the future?"
China's space launching market is controlled by state. In general, state owns all maket because PRC is a socialist state. The current commercial companies are established because the state openned up a sector of the launch service. This sector is middium payload. The sector of heavy payload is not oppened. Look at the commercial companies' protofolio, they compete with CZ-6, 8G, 8A and maybe 7 and 7A as these are in the catagory of commercial service. Nobody is going to make anything like CZ-9 and 10 without asking the state first.
Another more critical control by the state is launch site. All of them are in the hand of CASC. Land is state property. Any company needs state approval to build their own launch site, or need CASC approval to use existing site. So how could anyone develop any rockets without State approval in the first place? Someone can work in house on a CZ-9 class rocket even without government endorsement, but without a launch site what are they doing to do with it? Let alone finding a customer.
I will remind you again, this is China not USA. Things work in opposite order very often. In the US, SpaceX can develop whatever they want and buy a piece of land in Florida and build a site, the government can not say no except going through the same procedure as for NASA's launch facilities. In USA, money and private capital (SpaceX) is the ruler of the country. In China, state rules capital, government approves activities of capital, capital does what the government allows.