The problem for China is that they already had a large state agency doing this stuff. And they did it in a Soviet inspired way. They invest lots of money but their budget is tied up in many long term programs.
They can't just say 'well lets start from zero and copy SpaceX'. They have space station program that needs to continue and they can't wait until they have a next generation reusable rocket. Just like NASA they also do other things, like moon landers and so on.
And despite what people think, China can't infinitely invest in everything and don't. I'm sure the battles for money within China budgeting process are not that different from US congress.
Looking at ESA, getting budget for a new rocket is incredibly hard and ESA member states are richer then China.
Also I think its wrong to say there is no hardware secrets. Developing a very advanced rocket engine is really fucking hard, and to build one and be able to 'mass' produce it like SpaceX does is incredibly hard. Getting there took SpaceX a decade, and government run engine programs are nowhere near as fast usually.
The exact details of the heat shield and reentery of something like Starship also isn't exactly easy to replicate. Doable, but would still require quite a bit of reverse engineering.
SpaceX Starship production line isn't about 'one big secret' but about iteratively improving each part to make it cheaper and better over time. And you can''t replicate that without doing the same.