This map might make it easier to see how the tube reflects the geography, and so conjure a better image of London, but it makes using the tube system much harder.
As case in point, the fork in the Northern line at Kennington is much harder to comprehend and the number of tourists who get bewildered by this feature on the current map is large enough as it is.
It also still misrepresents a lot of the distances between stations, (Old St to Farringdon is a long way, much further than Old St or Moorgate to Liverpool St). If you are going for a concept of geographical correctness it has to be very exact or a complete abstraction.