I personally believe that singing psalms alone is significantly insufficient for Christian worship in the context of the New Covenant, under the gospel of Jesus Christ. For instance, Jews who oppose Jesus as the Messiah can happily sing these psalms while maintaining beliefs that are contrary to ours.
While I understand the necessity and obligation to read the Psalms (since they point to Christ, as per Luke 24:44), I am not convinced that it is compulsory to sing them without an accompanying musical score.
I have deep respect for all churches that perceive it as their moral obligation to create their own music scores (since the recorded Psalms do not include any) and incorporate these into their worship.
My only hope is that they would respectfully avoid imposing their personal moral obligations on other churches, and refrain from judging those who practice their faith differently. I earnestly hope that those who choose to sing Psalms in their worship and those who choose to sing new songs praising Jesus Christ would show mutual respect for each other.
Singing of Psalms is good but not obligatory. If it were obligatory, God would have preserved the musical scores along with the psalms.
Secondly, some of the psalms are dangerous to be sung during Christian worship, as many Christians who do not fully comprehend their historical and theological context will likely misapply the content to their personal lives.
Below are some examples of imprecatory psalms in which the psalmist cries out for curses and vengeance against their enemies in specific historical settings. Please imagine singing the following verses in a Christian worship session. What would non-believers perceive if they hear Christians singing these? Of course, I personally believe that all churches would have deliberately omitted singing these imprecatory psalms, or at least reduced their frequency.
Psa 109:9 May his children be fatherless and his wife a widow!10 May his children wander about and beg, seeking food far from the ruins they inhabit!
Psa 137:9 Blessed shall he be who takes your little ones and dashes them against the rock!
Psa 140:10 Let burning coals fall upon them! Let them be cast into fire, into miry pits, no more to rise!
Psa 143:12 And in your steadfast love you will cut off my enemies, and you will destroy all the adversaries of my soul, for I am your servant.
Psa 3:7 Arise, O LORD! Save me, O my God! For you strike all my enemies on the cheek; you break the teeth of the wicked.