As Wendigo said . You need basically only 1 Arcane Dome per Province
.
But with all other Domes there is a Problem : They are cost-ineffective . You can spam Mind hunt , costs only 2 astral pearls .
So even to destroy the Air Dome and Astral Dome Combo 10% of your Mind hunts get through the astral + air dome and thus destroy the air dome . So you can destroy the Domes cheaper then the costs the dome users have to pay . If the user can't make astral domes it is even worse cause then at average you only need 10 astral gems to destroy a 20 air gem costing air dome .