To offer a perspective from someone in the field: I built my career as a craftsman. Not just my livelihood, but my family’s livelihood depended on this craft. And within a few short months, my value has plummeted. I’ve tried to adapt, but I will never be as good with the newer tools as I was with the old, just like most carriage makers didn’t become mechanics, to use your analogy. At the same time, the value of the work is just less. Weavers could work in fabric mills, but their pay would be less. Now, just like back then, I, my wife, and my two young children face a financial reforming just beyond the horizon. It will be painful for many. There is no amount of adaptation that is within grasp of all those affected.
I think the general problem with your argument is that you assume that, because there was a transition from horses to cars, many people successfully transitioned from one profession to the other. The reality is that they didn’t. Many suffered in anonymity.