Your argument looks correct: being able to compute the value of the prior for any sentence you can represent is a very strong condition. In the boolean satisfiability setting this corresponds to P=NP, and in stronger settings it corresponds to incompleteness (e.g. you believe in ZFC, what’s your prior for CH?) On the other hand, you may cleverly maneuver so that all prior values you end up calculating in practice will be tractable, like in Monte Carlo AIXI.
Your argument looks correct: being able to compute the value of the prior for any sentence you can represent is a very strong condition. In the boolean satisfiability setting this corresponds to P=NP, and in stronger settings it corresponds to incompleteness (e.g. you believe in ZFC, what’s your prior for CH?) On the other hand, you may cleverly maneuver so that all prior values you end up calculating in practice will be tractable, like in Monte Carlo AIXI.