i think basically there is always only 1 dragon duke, so when the previous one dies another one is born (an egg appears?) so when they say they will just let him die/kill him, they are saying they are repeating the cycle they have started with this dragon duke (teaching him nothing and neglecting him). the dragon duke's existence in society can never go away since they will always be born after the previous dies, but the royals plan to use him as a symbol and instead of being under the dragon's thumb they will have the upper hand over him and always keep him weak
Oh that makes sense...
Or they wanted the duke to follow their commands... Since the current duke is stubborn and bull-headed, they want to make another one...
wasn't hereditary???
Do they plan to kill him so the next dragon duke will be born from amongst their family...?