I have noticed that the BCP 1662/1928 has a Psalter that is from the Coverdale Bible. Why was this never changed to the AV or any other translation. From what I can tell, it never changed from what Cranmer did in his editions...
I believe it was simply because the Psalter was too well liked to abandon for the Authorized Version. I wouldn't be surprised if there were more practical reasons, as well, but that's outside of my scope.