I don't know but I have always put it down to 2 reasons. Both are just conjecture
1, to create some airflow through the cockpit
2, decreases drag somehow
KERS, I always thought worked from taking unused energy during engine braking to spin up a flywheel via 2nd clutch on the front end of the engine (as opposed to the gearbox end) the flywheel is where it ends if you are using Mechanical KERS (Williams). Electro KERS has a smaller flywheel (I would imagine) and the rotational force is converted to electricity through a generator (like that alternator on a normal car) to charge a battery.
When the KERS button is pressed it will hit the clutch and the rotational force from the flywheel will help spin the engine faster. for Electro it also start the generator (this time acting like an electric motor) to help spin the engine.
afaik you're right about the hole giving some airflow through the cockpit, it might also reduce air pressure at the nose but I don't really know tbh.
I think the mechanical KERS uses a cvt (continuously variable transmission) to connect the flywheel to the drive instead of through a clutch.
I'm not really sure how the electric one works but I thought it would be some type of thermocouple that converted the heat from the braking into electric current which is then stored in the battery, then used to drive some sort of electric motor connected to the drive.
I didn't think the J-damper had been banned, Mclaren came up with the idea then Renault didn't quite understand how it worked and came up with the mass damper which was banned.
To use my phone in the car I deleted all my German contacts, it's now Hans free.