Are the engineering firms going to Chinese labs because of their rubber stamp approval or because the process is “tens of thousands” as opposed to “hundreds of thousands”?
The tests can be 100+ parameters and every single one is a hard binary pass/fail. So a mouse fart over the line on one test and you are not compliant. Go home, re-engineer, hope you fixed the issue (it's basically impossible to test for without a full dedicated RF testing chamber), and pay for a whole new testing run.
This is where the Chinese labs come in to play, as upon seeing your .5dB issue, they may feel that maybe their antenna placement was slightly off, or maybe you say that actually the "center of noise" (a bs thing) on your product is 5cm away from the testing center point, and move it back from the antenna with a wink and a nod.
In western labs the people are just as friendly, but that antenna is definitely in the right spot, and your product goes in the same spot as everyone elses.
However you need to go to China to do all this. If you are big megacorp with huge resources, western labs are fine. If you are smaller and possibly will become insolvent if you cannot pass testing, China is the play.