SE4 has a slightly different mechanic than most other shooters, in that a half-pull of the trigger will only show you shoulder-aim crosshairs, while a full pull will get you into ADS/scope.
In many other games, the half-pull will already get you into ADS - as the trigger there functions more like a dialog button (like the on/off buttons on the shoulders) as opposed to the analog triggers.
So even if it seems to "work" in other games, it may be that your controller is only registering a "half-pull" instead of the full pull you do - but for the other games, it makes no difference.
Since you stated that you switched L2 and R2, I assume you have a special/modded controller (or something like the Chronus/Titan Dongle). Some of the special controllers feature a trigger lock that basically limits you to pulling the trigger only halfway - so you can shoot and aim faster without having to fully pull the trigger. While this works for the above-mentioned reasons in most shooters, it does not work in SE4. If you have a special controller, check if it has trigger locks and how you can disable them or try the game with an original new/working controller (as I said, since most shooters make no difference between a full and a half trigger pull, your controller might seem like it works, but that doesn't have to be the case).
If you don't have a special controller (but can still switch L2 and R2), and you have a racing game or demo available, where you know that how far you pull the trigger determines how fast you go, try it out with your controller and see if you can get the full acceleration.