For anything short of a full race N/A motor, you really need some decent filter material in place, especially in a dry/ dusty environment where you are more likely to get fine airborne particles.
If you think of it as travelling on a road where other vehicles as well as your own have just disturbed and dispersed any dust lying on the surface into the air, and having a large air pump under your hood trying its best to suck it all in, that much is obvious.
Many aftermarket 'peformance' filters have dubious performance at either filtering OR flowing air, and are unable to prevent the finest particles being ingested by the engine. This can lead to accelerated wear of the engine internals and the compressor wheel, even if there is any kind of power gain.
Sometimes it isn't the stock filter or airbox capacity that is the problem but baffling built in to reduce air noise, and the aftermarket filter only works by sidestepping this. The best way to check for intake restriction must be checking through the intake for pressure drop with a manometer. (which will also show the truth about the filter as well)
Ripping out the stock airbox, filter and ducting and replacing with a cheap foam filter that then draws hot underbonnet air on a +T engine......good idea?..
If you haven't already guessed I'm not a great fan of foam type filters for several reasons.
If there is any question of the stock filter being restrictive on a high output motor, one option that hasn't been mentioned is the use of two stock paper elements. This can also be arranged in any way to fit available space, retains excellent filtering properties while doubling airflow potential, and is much cheaper than most of the aftermarket options.
As my new +T engine is having to draw intake air from a slot in the front of the car only about 8" above the road surface I'm making an aluminium airbox to carry two stock Fram panel elements from the VW Golf GTI who's dimensions just happen to fit the available space nicely. For the sake of a lttle DIY sheetmetal fabrication it is possible to have the best of both worlds.