There are people who preach, pray, and sing in ways that are entirely unedifying; the solution is not to get rid of preaching, praying. and singing, but to reform the practices.
These 3 elements are clearly commanded to be done in the Church in public worship in both dispensations of the covenant of grace, albeit differently (as with the sacraments). The onus is on those who wish to introduce/reintroduce/continue to use instruments in public worship to show that this is "expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture" (WCF 1.6). And so WCF Ch.21: "the acceptable way of worshipping the true God is instituted by himself, and so
limited to his own revealed will, that he may
not be worshipped
according to the imaginations and devices of men, or the suggestions of Satan, under any visible representations
or any other way not prescribed in the Holy Scripture) (21.1); "
Prayer with thanksgiving, being one special part of religious worship, is by God required of all men" (221.3), "The reading of the Scriptures with godly fear; the sound
preaching; and conscionable hearing of the Word, in obedience unto God with understanding, faith, and reverence;
singing of psalms with grace in the heart; as, also, the due administration and worthy receiving of the sacraments instituted by Christ;
are all parts of the ordinary religious worship of God (21.5). Just as there is no mention of instruments or uninspired songs in worship in Scripture since Christ's incarnation, there is also none in the Westminster Standards. I am not aware that there was even any debate about the use of instruments at Westminster - if someone knows of such a source, I would be very interested.