There is no pacification of the masses
You have to understand that the monarch holds no real power. Officially, yes, they can dissolve parliament or appoint a random person as prime minister, but if they get involved in politics at all, people ask "Who put you in charge?".
So, in reality, the royals do not exploit society in any way. They have no political power but delegate it the officials who "Just so happened" to be elected.
They are paid a salary by parliament but surrender profits from their lands to them. The profit is the higher figure, so even without tourism and branding they are good for the economy.
And, frankly, in tough times, they are always there and offer reassurance.
There is no subjugation and exploitation here except charging American tourists ridiculous prices for silly little trinkets