Low pass filters can have significant phase delay, whereas Kalman filters can be made to have essentially no lag (phase delay). Additionally, Kalman filters can stabilize the estimate of a state based off of other correlated measurements much better than simply low pass filtering the measurement.
For example, in an IMU, the accelerometers may be noisy due to vibration from the aircraft or vehicle, and the magnetometer measurements which are not affected by vibration, can be used to stabilize the inclination estimates.
Kalman filters are extremely useful and enable applications not possible with just low pass filtering.
Also, you don't need to get the covariance matrix "exactly right", these are tuned in practice on actual measurement and can be used to speed up or slow down the state estimation or weighting of different measurements.
For example, in an IMU, the accelerometers may be noisy due to vibration from the aircraft or vehicle, and the magnetometer measurements which are not affected by vibration, can be used to stabilize the inclination estimates.
Kalman filters are extremely useful and enable applications not possible with just low pass filtering.
Also, you don't need to get the covariance matrix "exactly right", these are tuned in practice on actual measurement and can be used to speed up or slow down the state estimation or weighting of different measurements.