First, I'm surprised that no one has brought up Revelation, which shows multiple uses of musical instruments -- gasp -- right before the throne of GOD! So, clearly there ARE cases of instrumental worship in the NT.
Second, the argument used above is an argument from silence. We have a very clear use of musical instruments of all types in the OT and that is bookended by instrumental use before God's throne in heaven. Silence between these bookends where instruments are clearly used ought not be taken as a "no instruments" doctrine, which is why most churches DO use musical instruments.
Third, I would suggest a lack of musical instrument use may be for the same reasons we don't always have instruments (or all of them) in our churches -- a mere lack of players and available instruments.
Rev 5:8-9 And when he had taken the scroll, the four living creatures and the twenty-four elders fell down before the Lamb, each holding a harp, and golden bowls full of incense, which are the prayers of the saints. And they sang a new song, saying, "Worthy are you to take the scroll and to open its seals, for you were slain, and by your blood you ransomed people for God from every tribe and language and people and nation,
Rev 8:2 Then I saw the seven angels who stand before God, and seven trumpets were given to them.
Rev 14:2-3 And I heard a voice from heaven like the roar of many waters and like the sound of loud thunder. The voice I heard was like the sound of harpists playing on their harps and they were singing a new song before the throne and before the four living creatures and before the elders. No one could learn that song except the 144,000 who had been redeemed from the earth.
Rev 15:2-3 And I saw what appeared to be a sea of glass mingled with fire--and also those who had conquered the beast and its image and the number of its name, standing beside the sea of glass with harps of God in their hands. And they sing the song of Moses, the servant of God, and the song of the Lamb, saying, "Great and amazing are your deeds, O Lord God the Almighty! Just and true are your ways, O King of the nations!