This article identifies the start of modern “praise and worship” sets to the Jesus People movement of the 1960s and '70s  .
Around this time hymn singing accompanied by organs and piano music began to be replaced by loud guitars, drums and tambourines, and repetitive “praise choruses”. Traditional hymns that reflect biblical theology and reverential worship of God (think Charles Wesley) seem to have been overtaken by pop-culture “happy-clappy” tunes and banal lyrics. That sentence is my personal opinion based on observation, by the way, and is not reflected in the article in the link above. Because the article is copyright protected I can only paraphrase parts of it.
The article points out that people sometimes conflate the rise of "praise music" with the rise of "Jesus Rock" and its later avatar, "Contemporary Christian Music" (CCM), which is misleading. Something called "Jesus Rock" was geared towards evangelism, apologetics, and entertainment. "Praise" music, on the other hand, was a mellower brand of music aimed at corporate worship.
Evangelical churches have now replaced hymnbooks with overhead projectors and “music worship teams,” whose function seems to be to get the congregation warmed up ready for the minister speaking for 20 or 30 minutes on a Bible subject. The music worship team play guitars and electronic keyboards (and other instruments) and repeat choruses over and over again (till older people like me have to sit down before they fall down).
Another article asks what theological credentials the leaders of this music industry have, and whether they are spiritually mature. The article concludes that “when worship becomes entertainment, and those that lead us in worship become performers and icons, then the gospel has been done a great disservice.” Copyright 2005: Adam Sparks worked for the Evangelical Alliance in the UK before moving to study for a PhD (Theology of Religions) at Bristol University.
This Christian believes that church worship should be God-centred, biblical, reverential, orderly, consecrated and balanced. In other words, the focus should be on prayer and preaching, with hand-picked hymns that reflect the main themes of the sermon being preached. As another Christian has commented, the "praise and worship set" is definitely not liturgical.
 The Jesus movement was an evangelical Christian movement that began on the West Coast of the United States in the late 1960s and early 1970s and primarily spread throughout North America, Europe, Central America, Australia and New Zealand, before it subsided in the late 1980s. https://en.wikipedia.org/wiki/Jesus_movement
 Jesus music, known as gospel beat music in the United Kingdom, is a style of Christian music that originated on the West Coast of the United States in the late 1960s and early 1970s. This musical genre developed in parallel to the Jesus movement. It outlasted the movement that spawned it and the Christian music industry began to eclipse it and absorb its musicians around 1975. https://en.wikipedia.org/wiki/Jesus_music
Edit: I didn’t become a Christian till 1996 and the U.K. Baptist church I attended sang traditional hymns accompanied by either a rather splendid pipe organ or a grand piano. There were no overhead projectors although the minister did allow younger people to play some modern songs to guitar and other instruments. At that time Maranatha Music was popular and I enjoyed songs like “The Servant King” by Graham Kendrick. I would consider that to be “praise music”. “Jesus Rock” music is unknown to me (it’s an age thing).
Anne may be onto something with regard to modern Pentecostal music although I suspect the rise of “mega-churches” might have signalled wider acceptance of this type of music. It is also worth remembering that “the music industry” exercises a great deal of power over what is broadcast and in lending financial and advertising support to promote “bands” or groups they think will turn a healthy profit. Please excuse my scepticism.
Alas, I am unable to find anything in response to your comment to me.