Because you can't have direct airflow in a supersonic inlet.
The airspeed of the incoming airstream needs to be subsonic or else it will cause the engine to flame out. All modern fighter inlets, be it fixed, variable or DSI all manipulates the airflow inside the inlet so that it bounces off of the inlet walls. This creates shock waves which slow the airflow to subsonic speeds when hitting the turbines.
When and where the redirected airflow hits the intake sides will vary depending on the way it is being redirected, which in turn depends on the speed of the aircraft (and hence airflow). As such, it will be near impossible to place an fuel cooling intake within the regular intake where it will get constant airflow.
I am not convinced those meshed openings are for fuel cooling, as you don't need two of them.
Some might scoff, but I still think those openings are to help regular airflow within the intake to work in concert to allow the J20 a much greater range of speeds than traditional DSI would allow.
The entire concept of DSI is to use the shape of the bump to manipulate airflow to achieve the above described dampening effect over a large band of airspeeds. Add two openings would allow the use of positive and negative pressure zones to vary when and where the airflow redirected by the bump first hits the inlet wall, which will cascade down and change the speed of the airflow when it hits the compressor face.
It's basically the same effect as traditional variable intakes, only you would be using pressure zones to shift the airflow rather than metal plates.
If this is really the case, I would love to see the 'experts' who dismissed this idea initially scramble to tell us which western concept the Chinese copied to achieve this innovation.