the major reason was to keep the city structure simple and repeatable, so as to reduce learning. This is one of the issues I found when my parents (even friends) visited NYC, the subway maps were too intimidating.
But simultaneously, the subcities are not repeatable in that the relationship between the intercity roads and the local infrastructure will be kinked; you need to adapt the circular intercity infrastructure (both the subway and local roads) to the rectilinear grid in three different ways over six satellite cities. That kind of variance may be desirable, but it will make it more difficult to memorize the layout and could introduce awkward kinks. Sometimes the circular perimeter roads will contact the principal city axis; in other cities they won't.