Analogue sticks are time-based, mice are distance-based.

Think of how you aim with an analogue stick. You hold the stick in a given direction, the camera begins moving in that direction, you wait until it's where you want and then fire. If you want to turn 180 degrees, you aim all the way to the left and wait until you've turned; usually this will take 2 or 3 seconds, because if the analogue stick moves too fast it becomes hard to aim carefully.

Then think of how a mouse works. You move the mouse a given distance and the cursor instantly moves that far, rather than waiting for the pan. If you want to do a 180 degree turn, you can whip the mouse 10cm to the side and you will instantly turn. This means that the camera control limitation is not limited by or based on the time it takes to pan (and on firing at the precise moment during a pan) but on your muscle memory, knowing how far to move your mouse to aim at any part of the environment -- if you're confident in your ability to aim you fire before even looking at what's under the reticle.

There's also the precision-speed tradeoff. If you make the analogue stick pan the camera too fast, repositioning is fast but imprecise; if you make it too slow, aiming is precise but slow. It's impossible to have precise and fast because that involves carefully watching for the tenth-of-a-second window where it's good to let go of the stick. With a mouse, all the camera movement is based on movements of your fingers and hands; we're very good at making careful fine movements with our hands to carefully get the camera exactly where you want it, but we can also make rapid jerks with our wrist to fling the camera around rapidly.

This means that certain combinations of mechanics aren't really compatible with gamepads. You can't have a game that requires hairpin-turn platforming or multidirectional 3D layouts that require elaborate camera control while also involving aiming and combat, because they require opposite sides of the precision/speed spectrum. With a mouse this would be possible but obviously you want an analogue stick for character movement in platform games which isn't easy to combine with a mouse.

An additional unrelated issue is that if you're using two analogue sticks to play, you've only got your index fingers on the triggers to use, while on a mouse+KB layout each finger on the keyboard can reach multiple buttons easily and there can be multiple buttons on the mouse as well.