Yes, the S air filter is way over kill for a 2.0/2.2 engine.
I put a restriction gauge in the intake tube to tell me when to change out my air filter and found that with the lid on I got 8"(H2o) of restriction and with the lid off I got none.
https://www.s2ki.com/forums/s2000-un...iction-921933/

I then put 90k miles on that air filter over 6 years and the restriction was still 8". I changed out the filter due to years of servive, not restriction.
https://www.s2ki.com/forums/s2000-un...ilter-1163927/
We have over 35k miles on this filter and it reads 0". I added a 2 3/4" or 3" hose to the end of the air box and ran that hose down to the fender well.
That got rid of the restriction that the stock air filter box had. Didn't change gas mileage or power(that I can feel anyway) but I wanted to to see if I could get rid of that restriction.

ROD

 

I put a shorter but typical size 6"x5" afe filter with the added center filter built in and started pulling vacuum at 7k rpm, so ditched that one and went with a larger then stock 8"x11". I wouldn't go any smaller then stock on this engine. Its sized appropriately. Definitely if you are sticking to more restrictive paper.

This engine breaths heavy at higher rpm, as much CFM as some v8's.

 

That makes sense, as 2 liter air pump at 9k rpm moves similar air as 4 liter air pump at half that rpm, 4.5k. ICE is basically an air pump.

 

How true, but take a look at a GT350(5.2L) and it out rev's a AP2 8250 to 8000 rpm's. The air filter on the GT350 is real close to the same size as the one in the S.
I'll say one thing about the GT350 is it has one of the best sounding engine I've heard.

ROD

 

Yeah that's right. the stock filter is sized appropriately for the engine's needs. I wouldn't go smaller than stock if I were to replace it. 9k rpm inhales a whole lot of air