Doc, why do you feel the movement is dying off?
Flippant answer: Because God's judging the leaders and church enmeshed in the error. Churches are struggling and pastors are horror story of what God would want in immorality, adultery, power struggles, financial ruin, empire building, homosexuality.
We've used names like Ruckman (on 3rd wife who divorced her husband - a student of Ruckman to marry him). Hyles (immoral, lying salvation by KJV or you are unsaved). Riplinger (uneducated woman leading men by the nose). And the list goes on.
More serious answer: It never was "big" in Baptist circles. Just a small part of the "independent fundamental Baptists" circle which is, of course, just a fraction of Baptists in the USA.
When teaching at Pillsbury Baptist College (Comparative Religions) we did some research on denominations within Christianity. Don't have the stats in front of me but will use general numbers -
15 million SBC
15 million Black conventions
4 million NBC and breakoff smaller groups
3 million "independent"
Of the last (IFB) less than a third or about 1 million people are in the "only" type of church, altho many of these are "preferred" and not true "only".
I get to travel the nation and have lots of contacts. I have never found an SBC or a Black convention KJVonly. May be a few, but tiny sliver.
I've met very few in the old NBC and other smaller organized groups of Baptists (GARBC, CBA, ABA, Missionary Baptist, etc) who were any sort of "only".
So "onlies" are big only in the small pond of Sword of the Lord, Ruckman, Hyles, some BBF churches. And in them, it is often the pastor, not the "sheeple" who just go along with it generally.
1 million (on the outside) v 40+ million non-only.
Movement created problems with Adventism where it originated and lost favor. Remember, cults NEED "authority" to control people, and especially "authority" that can be twisted/interpreted wildly as the KJV with archaic or words that have changed meaning in 400 years allows. Out here in Wyoming, Mormons do the same - take a verse and twist it but because people don't know what the old English meant (or worse - they THINK they know and it is 100% wrong) they flood them with false teaching.
Sadly, I've seen that from too many IFB churches, too. Pastors who don't know what God said, spouting to an even more-ignorant congregation and leading them into false doctrine.