I’m not sure what you mean. Are you suggesting that there are currently no such leaders?
In fact, as JustAServant pointed out, this has already happened. In the 1940s and 50s, many leaders of what had been called “fundamentalism” began replacing the term with “evangelical” (itself an older term that had never dropped out of use, of course–the point is that people began identifying themselves self-consciously as “evangelicals” as opposed to both “fundamentalists” and more liberal forms of Protestantism). Billy Graham was probably the most prominent of these, and cooperation with Catholics (and “mainline” Protestants) was one of the hallmarks of his evangelistic ministry, which brought him under fire from fundamentalists.
I wouldn’t say that the line is quite as sharp as JustAServant indicates. It’s quite fuzzy, and I wouldn’t say that Falwell “crossed from one to the other” so much as that he softened his fundamentalist stance a bit and began looking more like a very conservative “evangelical” (some would call him a “neofundamentalist”–I suppose, if the term doesn’t cause the English language to explode, you could call him a “liberal fundamentalist”

).
And evangelicalism is itself very unstable and always on the brink of flying apart. These days many younger evangelicals are very unhappy with the more “fundamentalist” aspects of evangelicalism (Biblical inerrancy, penal substitution, conservative social positions, the exclusivity of salvation through Jesus). Are these folks still evangelicals, or are they a new kind of liberal? Depends on your definition, of course:shrug:
But I think it is clear that old-fashioned fundamentalism of the BJU stamp is fading.
Edwin
Edwin