PostgreSQL: Why does this simple query not use the index?
This query can be performed using an optimization called a loose index scan. However PostgreSQL doesn't yet implement this optimization, so it uses a table scan instead.
Of the major databases, as far as I know only MySQL has implemented loose index scan (perhaps Oracle too?). PostgreSQL hasn't implemented this feature.
The query certainly can use an index. The reason that it doesn't in your particular case depends on the particular size and distribution of the data. You can use SET enable_seqscan TO off to investigate.
Because it requires scanning the entire table, so doing that via the index is of no benefit. ("Covering indices" aren't useful as a performance technique in PostgreSQL due to its MVCC implementation).