They are the exception though.
Not really.
A fwew years back, the CofS decided to create a new hymnbook.
The result was, and is, CH4, an amalgum of traditional hymns, metrical psalms, paraphrases, plus some modern stuff by Kendrick, Townend, Carter, etc, as well as Iona community hymns and world music.
The whole clamjamfrey is quite a good selection.
(Clamjamfrey = kit and kaboodle, obviously....)