"Milton Friedman's thermostat" is an excellent article (although most of the comments are clueless). But some things about it bear emphasising.

Output is set by some Stuff and a Control signal.

Yes.

Agent with full power over Control and accurate models of Output and Stuff can negate the influence of Stuff

No. Control systems do not work like that.

All the Agent needs to know is how to vary the Output to bring the thing to be controlled towards its desired value. It need not even be aware of any of the Stuff. It might or might not be helpful, but it is not necessary. The room thermostat does not: it simply turns the heating on when the temperature is below the set point and off when it is above. It neither knows nor cares what the ambient temperature is outside, whether the sun is shining on the building, how many people are in the room, or anything at all except the sensed temperature and the reference temperature.

You can make the Agent's beliefs inaccurate (directly, by showing the driver a video of an upcoming hill when there is none in front of the car, or by intervening on Stuff, like introducing a gust of wind the driver can't see, and then just not updating Agent's belief).

If you try to keep the speed of your car constant by deliberately compensating for the disturbances you can see, you will do a poor job of it. The Agent does not need to anticipate hills, and wind is invisible from inside a car. Instead all you have to do -- and all that an automatic cruise control does -- is measure the actual speed, compare it with the speed you want, and vary the accelerator pedal accordingly. The cruise control does not sense the gradient, head winds, tail winds, a dragging brake, or the number of passengers in the car. It doesn't need to. All it needs to do is sense the actual and desired speeds, and know how to vary the flow of fuel to bring the former closer to the latter. A simple PID controller is enough to do that.

This concept is absolutely fundamental to control systems. The controller can function, and function well, while knowing almost nothing. While you can design control systems that do -- or attempt to do -- the things you mention, sensing disturbances and computing the outputs required to counteract them, none of that is a prerequisite for control. Most control systems do without such refinements.