I have a PhD in NLP (which is what we often call it on the CS side, but is almost synonymous with CL="computational linguistics" on the cognitive/linguistics side of the field). I remember a talk at our annual conference, well-attended, perhaps around 2003 or so. The speaker was from one of the labs that was really leaning into "big data", which was only just becoming possible at that point, and argued persuasively that we should all just throw out our parsers and formalisms—ditch the computational linguistics side, basically—because we were on the edge of functionally infinite (unsupervised) data, and supervised and partially supervised systems would never ever be able to keep up. He presented performance numbers and how the unsupervised systems needed a lot more data to compete with the supervised systems, but that data was available, and he threw more and more and more data at the system and it got better and better. (I no longer remember the specific task he was using to illustrate his point.)
There were gasps in the room and a kind of depressed acquiescence: geez, he might be right. And the pendulum indeed swung in that direction, hard, and the field has been overwhelmingly dominated by the statistical machine learning folks on the CS side of the field, while the linguists kind of quietly keep the flame alive in their corner.
But I thought then, and I still think now, that it really just was another swing of the pendulum (which has gone back and forth a few times since the birth of the field in the 1960s). Perhaps it's now time again for someone to ring up the linguists and let them apply their expertise again?