A single paper cut won't kill you, but a thousand of them probably will. That's what people mean by "death by a thousand cuts". This is how many software projects die - it's usually a hundred little things that pile up, and whose combined pain becomes unbearable. It's the runaway bug list, the brittle test script that gets abandoned because it's too hard to maintain, the endless tedious validation on a details page, the component with the fuzzy interface, the buggy deployment, all the little features that just don't work right, etc...
This is why continuous integration, unit tests, automation, proactive team communication, code generation, good architecture, etc... are so important. These are the techniques and tools to prevent all those little cuts. I think that many of the current hot methodologies and tools are designed to add value not by doing the impossible, but by making the routine common tasks "just work", so that they no longer cause developers pain or stress.
The whole argument shifts from "is it possible" to "is it practical?" Then, hopefully your project won't suffer death from a thousand cuts.