If you want to know their personal motives, you will have to ask them.
I doubt that most full-time evolutionary theorists would say that the Modern Synthesis (aka neo-Darwinism) was “falsified” 50 years ago. I think they would say that the Modern Synthesis was modified, corrected, and extended to include a richer set of mechanisms, rather than simply declared false and set aside. I think they would say that variation, random mutation, and selection (all parts of neo-Darwinism) are still important components of modern evolutionary theory.
It seems, however, that most of the mechanisms proposed by modern evolutionary theorists would fall under the same ID criticism that neo-Darwinism does; i.e., they are unguided mechanisms, and the same ID doubts about the creative capacity of unguided mechanisms would obtain. So even if you could persuade Behe never to use the word “neo-Darwinian” again, he would make much the same criticism of most modern accounts of evolution, i.e., that unguided changes don’t have sufficient creative capacity to explain what we see. I don’t think he would believe that acknowledging most mutations to be neutral would help the situation very much, or that occasional accidental lateral transfers would help the situation very much.
Some ID folks have been less critical of the ideas of Gunter Wagner or Stuart Newman than of the others, probably because they perceive Wagner and Newman (rightly or wrongly) as upholding formalist or structuralist thinking, as opposed to resting heavily on random genetic changes. Denton in fact seems quite impressed with Wagner and cites Newman favorably. He actually seems to think that evolutionary theory has improved over the past 30 years! So it’s not as if all ID writers reject all proposals by all modern evolutionary biologists. It is mainly ideas, whether neo-Darwinian or later, that rely upon blind searches for adaptive success, that ID people are critical of.
And there is little doubt that, even though neo-Darwinism in its old form is no longer held by most, many biologists still place a lot of faith in the power of evolution to blind-search its way to successful new forms. As long as that is a major theme in modern evolutionary thought, whether it is called “neo-Darwinian” or something else, ID folks will oppose it. But any account of evolutionary change that sounds teleological, ID folks will be open to. And we’ve see in recent exchanges here that any account of evolution that has even a whiff of teleology, whether in Shapiro or Turner, still evokes massive and instinctive hostility from “mainstream” biologists. So you can talk all you want about how much evolutionary theory has changed from neo-Darwinism over the past 50 years, and you may be entirely right, but to the ID people, most of the changes (excepting possibly the ideas proposed by Wagner, Newman, etc.) don’t affect the anti-teleological character of the enterprise.
For good or evil, ID folks will never buy an account of evolution that is non-teleological. If “modern evolutionary theory” insists that evolution is without direction, without plan, without any internally proposed or externally imposed ends, it will continue to provoke the criticism of ID folks. You’ll get assent to common descent from some of them, but never to blanket rejection of teleology.