Should I hint table index for search query on wp_post

Question

I'm currently inspecting a WordPress setup with multiple custom post types that should be included into search results.

The database query for a search after the word Search looks like this:

SELECT SQL_CALC_FOUND_ROWS 
    wp_posts.ID
FROM 
    wp_posts
WHERE 
        1=1
    AND 
        (
            (
                (wp_posts.post_title LIKE '%Search%')
             OR (wp_posts.post_content LIKE '%Serach%')
            )
        )
    AND 
        wp_posts.post_type IN ('post', 'page', 'attachment', 'abbr', 'date', 'event', 'jobs', 'special', 'action', 'poll')
    AND
        ( 
            wp_posts.post_status = 'publish'
          OR 
            wp_posts.post_author = 28
          AND 
            wp_posts.post_status = 'private'
        )
ORDER BY 
    wp_posts.post_title LIKE '%Search%' DESC, 
    wp_posts.post_date DESC
LIMIT 0, 16

Here's the EXPLAIN result for this query:

+----+-------------+----------+------+------------------------------+------+---------+------+--------+-----------------------------+
| id | select_type | table    | type | possible_keys                | key  | key_len | ref  | rows   | Extra                       |
+----+-------------+----------+------+------------------------------+------+---------+------+--------+-----------------------------+
|  1 | SIMPLE      | ae_posts | ALL  | type_status_date,post_author | NULL | NULL    | NULL | 338315 | Using where; Using filesort |
+----+-------------+----------+------+------------------------------+------+---------+------+--------+-----------------------------+

The query runs about 5 to sometimes 8 seconds.

I played around a bit and found that MySQL uses the index type_status_date when the post_type IN () clause is changed to post_type = '' which of course is not a solution but it brought me to the idea to hint the usage of this key like this:

SELECT SQL_CALC_FOUND_ROWS 
    wp_posts.ID
FROM 
    wp_posts
FORCE INDEX
    ( type_status_date )
WHERE 
        1=1
//...

Which reduces the runtime at least to a third of the original value. Here's the EXPLAIN result:

+----+-------------+----------+-------+------------------+------------------+---------+------+--------+-----------------------------+
| id | select_type | table    | type  | possible_keys    | key              | key_len | ref  | rows   | Extra                       |
+----+-------------+----------+-------+------------------+------------------+---------+------+--------+-----------------------------+
|  1 | SIMPLE      | ae_posts | range | type_status_date | type_status_date | 164     | NULL | 145573 | Using where; Using filesort |
+----+-------------+----------+-------+------------------+------------------+---------+------+--------+-----------------------------+

The questions are: is it basically a good idea to force the usage of an index like this? Are there any possible negative side-effects? Is it typical for this type of query to ignore the index type_status_date or might there are some configuration issues on the server?