In postgres, distinct aggregates are a blind spot in the planner.

DISTINCT itself is handled well, e.g. "SELECT DISTINCT x, y ...".

But the distinct aggregates are not really seen by the planner, and they are always implemented with a sort. So this is a peculiar case for postgres.

One reason is because distinct aggregates can be more complicated to plan when you have a case like: "SELECT COUNT(distinct x), COUNT(distinct y) ..." because you actually need two different distinct sets as input.

Some databases have solutions for that problem, but postgres does not.