If labor was infinitely interchangeable, the price would go down. But it’s not...
Well, I was oversimplifying to illustrate a point, but the essential economics still stand. Labor is not infinitely interchangeable, but it doesn’t need to be so. It is interchangeable to one degree or another, which is enough to increase the supply.
All you can argue is that certain jobs or sectors might be affected less, or not at all, but the general effect doesn’t change.