I remember my music history class in bible college, and the tale that was told there about the transition from psalmnody to hymnody. A young Isaac Watts was sitting in church, being bothered by all the dirges he was hearing. That afternoon he complained to his father about them. "I could write better songs than that!" he claimed. "So let's see you do it!" was the reply, and he took up the challenge and started writing the hymnody that took the Christian church by storm.
But why was the church so ready to change? I would suggest that Watt's characterization of the psalms as dirges has a large part to play. When the genevans were written, they were sung in such a fresh and vigorous way that the Catholic queen of France called them the "Genevan Jigs". But as time went along, and as spiritual coldness began to set in over a couple generations, all that "frivolity" was despised and rejected by the psalm singers, who were too dignified to behave in such a way...
By the time Watts came around in the 1700s, this spiritual coldness was deep and wide, and was reflected in the music of the psalm singers. So when he started writing upbeat, doctrinally sound songs that the church could again sing with vigor, it won the day on a wide scale.
We have seen the same thing happen in our own day in the evangelical churches transition from hymnody to choruses. I grew up in it, and I remember the standard way that hymns were "supposed" to be done... slow and dirge-like. No wonder the choruses took over. The people of God need both spiritual vitality and vigorous, joyful music.
If we want to restore psalmnody to the church at large, it will be vigorous, word-for-word psalm versions that will win the day. It seems to me that anyone in whom the Spirit of God is doing a good work is eventually going to become tired of the shallow waters of modern evangelical music, and are going to be very receptive to the psalms being sung again. But it won't be to Genevans, sung slowly. Genevans with speed could be another story.