Short and simplified answer, liquid rocket engine is much more difficult to develop than solid engine. I even suspect that many Chinese "private" companies just source their solid boosters from missile producers which PLA is happy to spread out their cost.
It is unfair to compare SpaceX (or any US space company) with Chinese "private" launchers. The two countries work in totally different manners. In US, NASA would found private companies in conceptual and engineering work using state budget. Regardless who win the final mission, the private companies retain the owership of IP and experience of the state funded work. For example, SpaceX got the first crewed Artemis mission, that money is to finance partially Starship development. Even if SpaceX don't get any further mission, they are paid for research and can keep using that knowledge in anything they want. In China, "private" launchers don't get this money nor IP because they are not providing any work to state program. They have to pay for the knowledge through doing whatever job they can get which is pretty small compared to US counterparts.