It's probably true that many of these issues could be resolved without the need for this generic sets fantasy of mine. The resolution that you propose for Categorical{Rational} I think makes the right choice, given the tradeoffs that one currently has to make in designing these things.
The particular reason that I considered this issue to be related to the problem of the representation of sets is that if it is true that both the support of such a distribution and the values of the pdf were rationals one could support exact computation of moments and/or cumulants and/or coefficients of generating functions and the like. The "exactness" of these procedures becomes important if there is important information in the factorization of said moments/coefficients/whatever. In fact in these cases one actually might care to know not just that they are Rationals but Rationals with such and such restrictions, which is where more general type parameters would really start to shine. So perhaps someday somebody will want it...