If you're inserting one million rows, even 5 microseconds of parse and planning time per query is five extra seconds on a job that could be done in half a second.
Parsing is linear, planning gets exponential very quickly. It's got to consider data distribution, presence or not of indexes, output ordering, presence of foreign keys, uniqueness, and lots more I can't think of right now.
So, planning is much heavier than parsing (for any non-trivial query).
The table here is unconstrained (from the article "CREATE TABLE integers (value INTEGER);") but suppose that table had a primary key and a foreign key – a simple insertion of a single value into such a table would look trivial but consider what the query plan would look like as it verifies the PK and FK aren't violated. And maybe there are a couple of indexes to be updated as well. And a check constraint or three. Suddenly a simple INSERT of a literal value becomes quite involved under the skin.
(edit: and you can add possible triggers on the table)
CREATE TABLE integers (value INTEGER);