And where does Scripture impose upon itself the requirement of only singing "inspired" hymns or words? Where do the Psalms even do this?
It is considerations like this which forced me to abandon EP a few years ago.
The regulative principle requires a command to use uninspired song in worship in order for such song to be acceptable to God. The regulative principle of worship is simply the principle of sola scriptura applied to worship. So, the question ought to be, "Where does the Scripture *command* uninspired song?" If this is what you meant to ask, very good question indeed! Some have asserted arguments in this and other threads that this command is contained in the command to sing "New Song". In my opinion, this is very shaky grounds for justifying uninspired song. Others have a different opinion, and we will all stand before Christ with those opinions. There are, however, many possible interpretations of the phrase "New Song" in the Psalter, as so many have pointed out, both by giving their own opinions, and by citing the writings of some of the giants of the Church who have passed into glory. And, it is true that there are some other giants of the faith who held a contrary opinion. However, if it is exegetically plausible that the term "New Song" can refer to the Psalter itself, to Psalms being written at that time which were, in fact, "new", or if the "New Song" is not really temporally new at all, but new in the sense that we sing the Psalms with a New Covenant/Redemptive understanding, which corresponds to the command of the Apostle Paul in 1 Corinthians 14.16 and also Psalm 47.7, then we have an exegetical basis for understanding "New Song" as something different than uninspired song.
Further, one might ask which view comports best with the historical record of the Scriptures? Not wanting this post get get so long as to become burdensome, I would refer y'all to a study of the monarchy after the establishment of Psalmody by the sweet Psalmist of Israel, and especially to the reforming kings, as they re-established proper worship. At every instance, they instiituted the inspired Psalter for worship music, per the record of the prophets in 1,2 Chronicles. The same is true of the establishment after the exile--the returning exiles sang fdrom the Psalter, and there simply is no record of any other type of music being used.
The record of the New Testament is much the same, with the Apostle mentioning only the Psalms in his regulation of New testament worship in 1 Corinthians 14, and in the disputed passages of Colossians 3.16 and Ephesians 5.19 this three-fold synonymy has been conceded even by opponents of EP to refer to the Psalter. (See also Ephesians 2.2 and 6.12 for other examples of this kind of synonymy in Pauls writings)
Finally, I know these arguments will not convince those ensconced in their positions--that is not my aim, nor do I have the time nor the inclination to be drawn into a protracted debate. I write this overly long post only to show that we who do practice exclusive Psalmody do so from what we believe to be a comprehensive view of the Biblical data on worship song.