Because it clutters the map with a lot of unimportant information, makes it difficult to see county names at a glance, and makes it harder to see lieges?
I think knowing how the kingdoms are organized is a very important information. Right now I couldn't see when someone is granted/creating a new title except if I coincidentaly hover over the province. Maybe our playing styles are just different (on a side note: Have you played CK1?) but in the demo I have to click through several menus all the time to get info I saw directly on the map in the first game.
As for the 'map-cluttering' I don't see the problem: The map is almost empty right now, so there's not much what could be concealed by more CoAs.
Of what use is a clear map if I can't really do anything on it but have to go into the menus anyway?
Of course the best solution (but probably also the hardest to implement) would be to make it toggable with a button on the minimap.
Besides it wouldn't really hide anything and lieges would still be easy to spot because their CoAs are a lot bigger. The following picture illustrates how it would more or less look like: