Aren't you missing the entire point of exploratory data analysis? Eigenfaces are an example of what you can come up with as the end product of your data exploration, after you've tried many ways of looking at the data and determined that eigenfaces are useful.
Your whole third paragraph seems to be criticizing the core purpose of exploratory data analysis as though one should always be able to skip directly to the next phase of having a standardized representation. When entering a new problem domain, somebody needs to actually look at the data in a somewhat raw form. Using the strengths of the human vision system to get a rough idea of what the typical data looks like and the frequency and character of outliers isn't dumping the job of exploratory data analysis onto the reader, it's how the job actually gets done in the first place.
Your whole third paragraph seems to be criticizing the core purpose of exploratory data analysis as though one should always be able to skip directly to the next phase of having a standardized representation. When entering a new problem domain, somebody needs to actually look at the data in a somewhat raw form. Using the strengths of the human vision system to get a rough idea of what the typical data looks like and the frequency and character of outliers isn't dumping the job of exploratory data analysis onto the reader, it's how the job actually gets done in the first place.