I've been going to a Protestant Presbyterian church for 20 years now, with the metrical Scottish Psalter (led by a presentor) the only source of our musical worship up until 2010. It used the 1650 version approved by the Church of Scotland. I can only answer with regard to my particular denomination. Other Protestant Presbyterian groups may have other answers.
There was a special Plenary Assembly of 'my' denomination on 18th and 19th November 2010. I now quote from the official Statement issued from church headquarters. The event was
"to discuss and resolve the issue of sung praise. The Free Church, for
the last 100 years has been committed to the avoidance of uninspired
materials of praise and musical instruments, following what it
believed was the historical Reformed position on 'purity of worship'
and the Regulative Principle. Over the last five years though, some
Free Church ministers and office bearers have questioned whether this
position is the only scriptural one. After the Assembly asked the
Board of Trustees to set up a process for resolving the issue, it was
agreed that the matter would be concluded at a Plenary Assembly to be
composed of every minister plus an equal number of elders."
The main motion, which came from the Church's Board of Trustees, sought to retain the status quo, which is the
'avoidance of uninspired materials of praise and musical instruments',
but give more flexibility in understanding as to what is meant by
that. But this motion was opposed by Rev.… , who proposed that the
Free Church give liberty to individual congregations to sing
scriptural hymns, as well as psalms, if their elders so chose. The
debate, which lasted Thursday evening and most of Friday, was
harmonious throughout. Rev....'s motion carried by a majority of 98 to
Because the 12-point 'Finding of Assembly' is so long a document, I will not copy it here, but I extract these points from it:
Based on the declaration that purity of worship requires that every aspect of worship services, including sung praise, be consistent with the Word of God and with the whole doctrine of the Confession of Faith approved by previous Assemblies, ordained that every service of congregational worship would include the singing of Psalms. Individual congregations could restrict the sung praise to the Psalms, or to include paraphrases of Scripture, and hymns and spiritual songs consistent with the doctrine of the Confession of Faith, and have freedom to permit musical accompaniment to the sung praise in worship, or not. Further, a visiting minister, presiding at a service where such changes had been enacted could exercise freedom not to have those changes.
The next steps were taken by individual congregations of the denomination. Stage 1 - Kirk Session discussion, Stage 2 - Congregational consultation, Stage 3 Congregational meeting and Kirk Session decision. Different congregations came to different decisions, so you will find some sticking to purely unaccompanied Psalm singing, while others will have those plus other spiritual songs (usually with musical accompaniment.)
Our congregation voted by a clear majority to introduce 'uninspired' words of hymns, with keyboard accompaniment. The recurring reason given by those in favour (which I heard with my own ears) was that they longed to sing the Saviour's name in their sung praise. They wanted to praise the name of Jesus, who is only obliquely referred to in the Psalms (as the promised Messiah). Given that he has now come and is glorified in heaven, with all heaven singing the praises of him who sits on the throne AND the Lamb at the centre of the throne (Revelation 5:6-14 & 7:10-12 & 17 plus 22:1-3), it is fitting for Christians to sing about Jesus Christ, directly. The name of Jesus Christ is inspired, and inspiring. There was also reference to how the musical and poetic gifts of king David, and others, was not restricted only to them, centuries ago, with any kind of law that no others must compose worship music and verse. Heaven's throngs sing and nobody should be surprised, upon arriving there, that they sing new songs (Revelation 5:9) along with old ones (Revelation 15:3). Such views are also common in other Protestant Presbyterian denominations that have expanded their sung praise.
Despite our majority desire, two elders who objected said they would have to resign if the change was enacted, leaving our congregation with insufficient elders to 'run' it. Our of regard for them, no change happened. Yet, later, it did - I know not why. Perhaps some other elders had a word in their ear about blackmail?
I am very aware that this answer does not provide many reasons for this event, but that is because I was not privy to the debate, nor do I have the complete text which was made available by a local elder as well as being on the official denominational website eight years ago. I do not know if it is still on-line. As I was not brought up with the Scottish Psalter, only starting hymn-singing to an organ or piano from my mid-20s onward, and then only the Scottish Psalter 15 years later, and now a mixture of both these past eight years, I simply want to just sing to the Lord my God with a full heart, singing scripturally sound words. I have been known to stop singing at certain points in certain hymns, and a few modern 'choruses' I just will not sing at all. It can be a bit of a mine-field, I know, but the alternative is staying hunkered down in the trenches of 1650. But those last three sentences are merely my personal opinion. If pedants on here want me to remove them, otherwise they will remove my entire answer, I simply mention that that - precisely - exemplifies the entire problem with this vexed question of whether to use only the Psalter, or not.