Not so - look at the deployments to BH, Afghanistan & Iraq to see that that is simply not true. The government is frequently incapable of defining missions for military operations.Depends what the mission is. If the mission is to provide the King's Trop RHA and the HCR Mounted Regt for ceremonial duties I'd say that the donkeys are not just essential but mission critical.
We, as soldiers, don't define the mission. The government, on behalf of the nation does that and the Government wants ceremonial. If they want us to empty bins, fight fires, make flood defences or dispose of mad cows then that's the mission