Not a robotics expert. But my understanding of the effect of input/motion models on the state estimation of Kalman filters is that it conditions the error covar

Not a robotics expert. But my understanding of the effect of input/motion models on the state estimation of Kalman filters is that it conditions the error covariance of the state estimate. So, when the quality of measurements is very high (almost no noise), then the motion model provides very little benefit. And when the measurement quality is very low, the motion model reduces the error ellipse around the real state of the system. So, even when there are inputs and a motion model you could imagine the Kalman Filter as a frequency-domain filter (E.G. IIR/FIR filter), where the tap weights are being updated based on some known function. If the quality of the measurements are high enough, and the sampling frequency is high enough. Then the Kalman filter should be able to converge to a very good estimate of state, even with no motion model right? In which case it would have the exact same characteristics as an adaptive, slowly time-varying frequency-domain filter.