As far as fuel economy claims go, no air filter can improve that because right behind the air filter is the Mass Airflow Sensor. The fuel injection is then set to deliver the optimal 14.7 to 1 ratio based on the airflow. You can completely remove the air filter with no increase in economy.
The air cleaner can limit peak performance by acting as a sort of throttle, limiting airflow. However, the engineers have already designed everything around the limiting factor, usually the engine valve system. There isn't much margin left to exploit in either the intake or exhaust.
With the competition to produce the most powerful and economic vehicles, can you imagine an engineer overlooking the air cleaner for additional performance? Not a chance. If that's all it takes to improve performance, even a tiny amount, they'll install it and claim they're better than the other guy.
There are applications where an oily cotton rag makes a good air cleaner, such as motorcycles, lawn mowers, etc., where high airflow in a compact area is needed, and routine maintenance is not a concern.