Okay, forgive me if someone's already posted on the topic, but there's a contradiction in the logic:
"Motion controls, meanwhile, are thought → large movement → however long it takes for the console to register that movement → action. It's not immersive, it's going in completely the opposite direction to being immersive."
If I understand this statement correctly, it would appear that your primary objection to a motion controller is that since there's a delay from when the motion is made to when the game registers the motion, the delay will prevent immersion.
This logic ignores the elephant in the room that the current controller ITSELF is ANTI-immersive. Your standard controller with X, Y, A, B, Circle, Triangle, etc. buttons and its two analog sticks and whatnot is a bewildering array of strangeness that doesn't follow intuitively. I still don't know why they don't label the buttons something that makes sense, like North-South-East-West, so I could freakin' FIND them. I'm a twenty-year veteran of video gaming, and I kept getting killed in Brutal Legend because I couldn't tell the Y button from the A button fast enough. A player loses all sense of immersion in Heavy Rain when they have to look away from the screen and down at the controller to figure out which one is the square button.
Whereas in Zelda: Twilight Princess, the motion for drawing the sword was simply to flick the Wiimote. To swing the sword later, another flick of the Wiimote. The action felt like swinging a sword at someone. It was easy to remember, and it was fun. And most of all, it was more immersive than any button press or trigger-flick.
The Wiimote does one thing better than all of its rivals -- the shooter. You yourself have said that the console-shooter can't stand up to the PC-shooter because it lacks a mouse. The Wiimote lets you point directly at your widescreen TV and plant a bullet exactly where you want it. And by definition, pointing at the screen is more immersive than pushing a little plastic puck somewhere near the screen.
The issue here is with the logic. You're arguing that motion controls are anti-immersive because your sense of immersion breaks when you want to blame the controller's lag time for your failure to accomplish something in the game. That is a valid complaint. But it's no different than a sticky button on a controller -- bad equipment is simply bad equipment. When a motion control is spot on, it's far more intuitive than "Press Y to not die". Raising a sword to block a bullet feels more real when you're raising something to block.
Granted, the current crop of motion-controlled games are far, far too gimmicky. Then again, the video game market right now is dripping with gimmickry, as the still-enduring "quick time event" is still present. (Motion-controller or button-controller, it didn't matter to Ninja Blade -- even if you pushed right, the dodge was always to the left.) As the Wii is maturing, there's a lot more shooters coming out, and the wiimote-with-analog numchuk is simply more intuitive than shooting by moving a little airplane flight stick.
The motion-controller is seen as the future because the current controller is complicated to the point of baroque ridiculousness, where only a hardcore gamer can be bothered to memorize every button. What we really need are games that work with the motion controls, instead of gimmicks that just happen to use motion controls. Oh, and more responsive motion controls wouldn't hurt, either.