It's obvious they don't trust any of the Chinese Americans

That's why they can't spy on China anymore.

The golden rule of espionage is that your enemy is gonna spy on you as well. So it's incumbent on you to go on the offensive and spy even harder.

The kind of person who can spy on China or, say, the Soviet Union speaks the local language, and has economic and political ties with local assets. Both the spy and the assets are gonna play a double game if for no other reason than the fact that they can make more money that way.

The US played that game well all throught the Cold War. And it chose to lose the capability to do so after the Aldritch Ames Incident. The americans have gone on the defensive, and are more focused on ensuring the enemy can't spy on them at all. As a result the espionage officers can't be perfect for the job - hiring a well connected person is too much of a risk - and the espionage assets aren't hired in the first place. What CIA agents the US had abroad were legacy agents from a more daring time. And all those guys were purged when the Iranians found a security breach in the american intelligence networks, got the informants' names and sent the list to Russia and China.