It is a difficult proposition for the Christian to object to singing the Bible, even if the OT. To excise songs of the OT would require an assumption of critical discontinuity between the dispensations of the covenant of grace. Certainly, elements of discontinuity exist between the dispensations of the one covenant of grace, but do they exclude certain of the psalms?
Poundstone's objection to the imprecatory psalms focuses on the NT command to love your enemies. To assume this command a discontinuity with the OT remains suspect. Within the context, Jesus is merely restating the OT law and putting in back into its original state without the accretions it had accumulated through the traditions of the elders. Of course the critical question is the existence of prayers of imprecation in the NT. For this, I would draw your attention to a few passages.
"If any man love not the Lord Jesus Christ, let him be Anathema Maranatha." (1Cor. 16:22)
"But though we, or an angel from heaven, preach any other gospel unto you than that which we have preached unto you, let him be accursed. As we said before, so say I now again, If any man preach any other gospel unto you than that ye have received, let him be accursed." (Gal 1:8-9)
"And when he had opened the fifth seal, I saw under the altar the souls of them that were slain for the word of God, and for the testimony which they held: and they cried with a loud voice, saying, How long, O Lord, holy and true, dost thou not judge and avenge our blood on them that dwell on the earth?" (Rev.6:9-10)
I find unconvincing the argument that prayers of imprecation, properly understood, have no place in the Christian life.
Poundstone's second argument suggests that the Christian's emotional response to evil, especially persecution, differs from that of the psalms. While certainly, we have more reason to trust in God and see in Christ our example for suffering, the Bible does not give any suggestion that our emotional experience differs. If persecution and evil did not hurt, they would not be called suffering. The Puritans called it the "dark night of the soul." To strike such psalms from our understanding suggests a superficial approach to suffering, one out of sync with the realities of the NT and the history of the church.
The best argument against the psalter is the attitude toward the nations. Howbeit, the way the psalms normally display this hostility is in the midst of the declaration of the history of Israel and the triumph God gave them over their enemies. Those stories give us hope that as He has done in the past, so in the future, God will triumph over His and our enemies. (WSC 26) Understood properly, the psalms record the privilege that God's people have over all other people groups.
The final matter is that of the future life which Poundstone finds absent from four (4) parts of the Psalter. This does not define the whole tenor of the psalms. (see Ps.139:8) In those occasions he mentions, the context is the cry for relief from suffering. The petition suggests that the believer cannot praise God in the land of the living if dead. To say this argument lacks a future hope seems oddly disjointed from the teaching of the OT.
Regarding giving David a Christian voice, Poundstone suggests that Isaac Watts was right in taking the Psalms and "christianizing" them, that is, changing the expressions from one of a future hope of the Messiah to a past celebration of the Messiah. Absent this, Poundstone argues that this denies David a Christian voice. Giving David a Christian voice is clearly anachronistic. Letting David speak his faith in God which we share allows scripture to speak. I do not denigrate the work of Isaac Watts. Indeed, it is a laudable and beneficial part of Christian hymnody, but it is not giving David a Christian voice. It is Isaac Watts using David's words to express Watts' Christian faith. This is the work of a good pastor, but ought not denigrate the underlying scripture. The sermon does not replace the scripture.
I would admit that the psalms are insufficient hymnody. That is why we are not exclusive psalm singers. After all, the revelation of the NT includes what appear to be hymns of the NT church that do not arise from the Psalms. The Psalms do demonstrate a lack of the complete revelation of scripture. A Psalter-hymnal ought not replace our hymnals but augment them. Our current hymnal does not have the totality of the psalms and some of the ones it does have contain unfortunate or misleading readings. The proposed psalter-hymnal contain all of them with variation in text and tune. I cannot formulate an argument that would deny the utility of the project so long as its limitations are observed.