Yeah, I agree with the point that classical logic would instantly settle all digits of pi, so it can't be the basis of a theory that would let us bet on digits of pi. But that's probably not the only reason why we want a theory of logical uncertainty. The value of a digit of pi is always provable (because it's a quantifier-free statement), but our math intuition also allows us to bet on things like Con(PA), which is independent, or P!=NP, for which we don't know if it's independent. You may or may not want a theory of logical uncertainty that can cover all three cases uniformly.