The command to sing is specific. It does not leave room for mechanical instruments. If we only had a general command to praise God, then anything would be allowed. However, we are told specifically how to praise God. It is by singing and making melody in our hearts.
And somehow having a piano in the room negates that?
Tell me, does the command to sing leave room to use songbooks? My bible certainly doesn't specifically authorize the use of written records of hymns, and while we do have written records of the lyrics of the psalms, these are without down Old Covenant writings and therefore do not apply. There is of course the New Covenant command to sing "...hymns, songs, and spiritual songs" as recorded in Ephesians 5 and Colossians 3, but these passages do not permit songbooks any more than they allow instruments, and it's likely that the first-century church didn't use songbooks.
When you say "The command to sing is specific. It does not leave room for mechanical instruments," I reply "Says you." If you can't cite any biblical authority for your position, I'm afraid there's no reason why I should respect that position. Show me in the Word of God where instruments are forbidden...or, failing that, show me in the Word of God where your approach to the scriptures that pertain to the issue is prescribed. If you can't do that, you're standing on your own authority, or that of the people who taught you, and that won't sway anyone. Nor should it.