I could take the encoders out and the robot would work fine. Its position would just grow increasingly inaccurate over time and make the production line more fragile. It would also make writing the pick n place code a bit of a pain for several reasons, but they're not fundamental to the design.
I mean... the robot would decidedly not work fine without joint encoders, on any timescale relevant to the task. You likely could not accomplish one pick/place operation. You need the position feedback because you don't have a good enough model of the motors (and everything) to do feedforward control alone. So I'd say position feedback is pretty fundamental to the design. (If you have stepper motors, then okay, you do have a good enough model of the motors.)
I think I agree with your point at large, though, that the "proprioceptive" sensors of the robot don't have anything to do with the environment the robot is in, or the task at hand.
But now what about an air conditioner with a thermostat? That's got a sensor and an actuator and the sensor in this case really is fundamental to the task at hand.
A toilet cistern would also qualify. (And in fact, while I wouldn't deem it a robot, I often use this as the simplest possible control system example.)
nope, encoders are definitely fundamental. You cannot give a DC (brushed or not) motor voltage and have it turn a fixed distance. The closest thing is steppers, but once they stall, you've lost feedback and positioning information.
