We can solve the Riccati equation and get the steady state priors for a Kalman filter.
So why are people still allowed to have any prior they want? They can solve Riccati equation ex-ante and use the steady state prior as the initial value, and reach steady state at time 0 rather than time infinity. And this is the only 'right' prior any rational individual would use.
I understand this is a philosophical question, any comment is welcome.