Interesting! I wonder how it would work on other kinds of data. For example, take a checkerboard image, rotate it (by, say, 15 degrees) and then seriate the result. What will it look like?
Should be easy to try! My expectation is that the TSP approach would recover the original image unless you added a lot of noise to it. Adjacent rows will still end up extremely similar to each other.
My expectation is that it wouldn't, because in a tilted checkerboard image (or any other periodic image) there are many pairs of rows that are more similar than neighbors.