For the reasons indicated (that is, MVCC), PG can not do a DISTINCT or the equivalent
GROUP BY from index values alone.
If this table is large, perhaps you could denormalize and maintain a
summary table with date (using truncation) and count, updated with
triggers on the original table. This table will presumably have a
small number of rows at the cost of doubling the times for updates,
inserts, and deletes.
