Precisely. If you had researched it, you would know that the shaft is solid all the way through with what amounts to a strain gauge to measure torque on the wheel and a closed feedback loop to apply force to reduce that torque. The sensor is electronic, not purely mechanical. Other than that, it is fundamentally the same implementation and failsafe as 95% of the vehicles on the road today. There are people who think that electronic sensors are bad, but they are often the same ones who think carbs are better than fuel injection.
And where is the evidence about the brakes having any relation to the steering? Yes, it has a connection to the CAN bus. Where it reads the vehicle speed to allow for clever tricks. You could just as easily ask why the radio needs to know that the brakes are on because it is also connected to the CAN bus. Or why the engine computer needs to know that the turn signals are on.
I've researched quite a bit which is why I pulled a column and module from a 2010 Corolla back in September. $62 at the Pick Your Part for power steering with (hopefully) much less hassle than moving the steering box and adding a pump! I also thought about going the hydraulic route using an electric p/s pump from a Volvo but I would still have to get a new steering box. I've read that the Volvo pumps sound like the whine from the DeLorean in Back to the Future and would rather not have that (although that would sound neat like once). The EPS just makes sense.
You are right about all of the connections (brakes, speed, etc.), they are there only to increase or decrease the assist in certain situations and are not needed unless you want adaptive steering. The failsafe mode works at the same assist level needed for around 40 MPH at all times. I'm perfectly fine with that.
These are the Toyota/Nissan/Kia units that have built-in failsafe. GM units can be used but require the use of another module that tricks the unit into thinking the vehicle is travelling at a certain speed and have a potentiometer that makes for adjustable assist but I personally don't want that extra layer of complexity.
'04-'09 Prius
'06-'11 Yaris
'07-'09 Versa
'08-'11 Scion
'09-'13 Corolla
'09-'12 Cube
'12-'14 Soul