It’s not wrong to write a new song or compose devotional poetry.
Amazing Grace is a good poem, and it can be sung to remind us of spiritual truths. Such poems and songs do not add to the Bible. At least, they ought not to be used in such a way.
The central issue is God’s command concerning
worship. To sing songs other than those that God has given is to add to - or neglect - God’s command. If God’s command is to sing psalms and psalms only, then singing anything else, because it dishonours that command, would indeed be akin to adding to Scripture.
What would you say if your pastor delivered a sermon based on a book other than the Bible? It might be a really good book, a solid Christian book. But you can’t set it up in the place that God has given to his own word. (Years ago, I sat in church and heard to a sermon that was merely a summary of Randy Alcorn’s
Heaven. It felt pretty weird.)
The mistake that so many make is to find a devotional poem or song and then decide to make use of it as
worship because…
why not? That is simply the wrong place to start. “Why not?” does not regulate the church’s worship. God does.
A song may not be errant in itself - though many hymns and other so-called worship songs do contain theological error (you don’t get that with the psalms, by the way). Very commonly, the error lies in how the thing is used. (Sort of like guns, I suppose!)
If you have an old lady in your congregation who likes to write devotional poems, there’s no need to discourage her! Just don’t get everyone singing them and calling it worship.