Finding "most recent" using daterange

Coming back to PostgreSQL after a (decades-)long absence...  If I have
something like:

CREATE TABLE example (
id integer NOT NULL,
value text NOT NULL,
dates daterange NOT NULL
);

INSERT INTO example VALUES
(1, 'a', '[2010-01-01,2020-01-01)'),
(1, 'b', '[2010-01-01,)'),
(1, 'c', '[,2021-01-01)'),
(2, 'd', '[2010-01-01,2021-01-01)'),
(2, 'e', '[2015-01-01,2020-01-01)'),
(3, 'f', '[2014-01-01,2016-01-01)'),
(3, 'g', '[2013-01-01,)'),
(3, 'h', '[2012-01-01,)'),
(3, 'i', '[2013-01-01,2017-01-01)'),
(4, 'j', '[2010-01-01,2015-01-01)');

and I want to find the "most recent" value out of each group, meaning
that having the greatest upper bound followed by the greatest lower
bound, what I've managed to come up with thus far is:

WITH intermediate AS (
SELECT e.id, e.value, e.dates
FROM example AS e
JOIN (
SELECT id, max(coalesce(upper(dates), 'infinity')) AS max_date
FROM example GROUP BY id
) AS max_upper ON e.id = max_upper.id
AND coalesce(upper(dates), 'infinity') = max_upper.max_date
)
SELECT i.id, i.value, i.dates
FROM intermediate AS i
JOIN (
SELECT id, max(coalesce(lower(dates), '-infinity')) AS max_date
FROM intermediate GROUP BY id
) AS max_lower ON i.id = max_lower.id
AND coalesce(lower(dates), '-infinity') = max_lower.max_date;

which produces the desired result for this minimal example:

id | value | dates
----+-------+-------------------------
1 | b | [2010-01-01,)
2 | d | [2010-01-01,2021-01-01)
3 | g | [2013-01-01,)
4 | j | [2010-01-01,2015-01-01)

I pretty quickly discovered that there's no max(daterange) -- although
it isn't obvious what that would do, anyway -- and the "intermediate"
CTE is what followed. Is there a better way?

(Note that this doesn't try to handle duplicate ranges -- I haven't
decided whether that'll be necessary in the real case. Assume it'll
have something beyond daterange NOT NULL and/or some _agg() magic,
eventually.)

-Rob