How to make MySQL using an index only by adding "order by"

Code

-- tested with MySQL 5.6

-- Type ALL - no index used.
EXPLAIN SELECT h.date, h.price, h.name FROM history h
    JOIN history h1 ON h.id = h1.id;

-- at least, it uses index now and no sort in Extra
EXPLAIN SELECT h.date, h.price, h.name FROM history h
    JOIN history h1 ON h.id = h1.id
    ORDER BY h.id;

Result

id	select_type	table	partitions	type	possible_keys	key	key_len	ref	rows	filtered	Extra
1	SIMPLE	h	null	ALL	PRIMARY	null	null	null	1407	100	null
1	SIMPLE	h1	null	eq_ref	PRIMARY	PRIMARY	4	my_schema.h.id	1	100	Using index

id	select_type	table	partitions	type	possible_keys	key	key_len	ref	rows	filtered	Extra
1	SIMPLE	h	null	index	PRIMARY	PRIMARY	4	null	1407	100	null
1	SIMPLE	h1	null	eq_ref	PRIMARY	PRIMARY	4	my_schema.h.id	1	100	Using index

More Snippets

Instead of MySQL's IFNULL function, this works on PostgreSQL, Sqlite and others too
Prevent a temporary DB table caused by SQL group by
Not equal where condition on index as a performance problem

Used Versions

PHP 8.2, Laminas MVC 3.2, Symfony 5.2, Laravel 8.28, PHPUnit 9.5, Doctrine ORM 2.8