Back when carburetors were the primary fuel delivery device, there was some validity to CAI. Since at any given steady fuel flow, lowering the temperature of the inlet air could would have some direct impact on air density, but fuel to air ratio would be at the mercy of fixed carburetor jetting. Re-jetting to lower fuel ratio and lower the inlet air temperature will (did) produce cylinder "packing" and a performance gain would be measurable.
Today's fuel injection systems monitor the inlet air temperature and maintain the air fuel ratio across the designed operating range. As you lower the inlet air temperature, whether artificially or naturally, a fairly steady air fuel ratio is maintained. Thus, in this respect, there is no gain to CAI.
Nor does a CAI allow more air into a factory designed intake system on a stock engine. The engine is not an air pump. Air "fills" the engine's cylinders solely by atmospheric pressure and adding a CAI cannot get more air past the engines chokepoint, which in a lot of cases in the throttlebody. Again, as atmospheric pressure changes, modern systems adjust the air fuel ratio accordingly.
There MAY be one advantage that works on some engines, and that is removing air turbulence from the effects of ribbed flex tube inlet plumbing like is used on the Hemis and a lot of other engines. However, I suspect it may be extremely marginal.
Just my opinion, but the only beneficial outcome of CAI is the redistribution of wealth.
Regards,
Dusty
2019 Ram 1500 Billet Silver Quad Cab 2WD, 5.7 Hemi, 8HP75, 3.21 axle, 33-gallon fuel tank, factory dual exhaust, 18” wheels. Build date: 3 June 2018. Now at 79181 miles