Here a suggestions. It would be to make all discovered map quests and mines available for each kingdom whoever owns the city beside it, heres why :
Game is currently unbalanced for lower-city kingdom, the dominant kingdom will get the most ressources which will lead to it to evolve faster eventually crushing others without any chances for them to resist. This generally lead to a one-kingdom server where all players migrate to the strongest one and hope to farm all map. Most of old servers are like this right now, mostly in hope to gather most resources before the server merge.
Making quest available for all would remove that current benefit and would allow weaker/defeated kingdom to still gather strength in hope to resist in the future.
Removing the 10 cities count requirement for king is a good step toward that.
Now why would be capture cities if we don't need them anymore for quest/mines:
Well first the territory bonus which lead to 100% recovery rate is already a good advantage to the one owning a city beside a quest, add-in cities bonus. plunder ability and the 100% recovery duel these are enough incentive to own a city. If that is not enough, maybe add a 10% timer bonus on the quest/mine for the owner, but I believe that would not be necessary at all.