What influence? Over neighboring states, systems (valid in case of T-31) and Houses (over Rheinland).
Bretonia has sufficient power left in the form of a large military (represented by the fact it has the same amount of battleships as the rest) and is using diplomacy as a means to gain more.
Houses fighting for resources and to make sure their counterpart remains weak has been the theme of the game since vanilla, and there's little reason to change it.
