With lots of testing, yes, you can incrementally build a working system that you don't understand. But by myopically staring at diffs all day, you'll only get farther from the truth of how your system works.
The major refactors that I do, are because I've come to the realization that my data model was not correct. A realization, that often happens multiple times during a project. My utility functions are still useful, but I have to rewire everything. There is no meaningful way to do that incrementally. Why would you even try to do that incrementally? It's like, if you have a salamander and you want to turn it into a horse incrementally. Of course, most of the RNA is the same. But testing and code reviewing the steps between salamander and horse seems to me like a waste of time.