Thanks very much.
I think another problem is that the cost estimation isn't good enough to reflex real cost. Since we can see, from "explain analyze ...", count(distinct ...) has smallest cost between the others, but since it uses sorts, the time complexity should be higher especially for large amount of rows.
Also I think even if we can have multiple count() expressions, the optimizer should also be able to choose between use sort, HashAggregate or maybe something like linear aggregate if sorts are not needed or other methods if exist. Also this may be done as just one job for entire table of interested columns, or for each column separately.
regards,
jacket41142