I don't know anything about the TRD filter, but did grow up when all cars used oil bath air cleaners. When the paper filters came in two advantages were cited -- easier maintenance (since cleaning an oil bath cleaner is messy!) and much better filtration. The paper filter blocks the dirt, which is why it gets more restrictive over time and needs to be replaced. The oil bath relies on the stickiness catching the dirt particles, but much more particles will get through.

So I can see a benefit for racing, but in everyday driving I expect you would be trading slightly improved performance for reduced engine life.