Nah... that I get...
1- They have tools to detect when power is used, like whe she used at duke's house so guards wehe on the way.
2- As said... guards were on the way so not enough time... sadly.
3- It would be even more traumatic for the baby seeing the duke killing someone and he'd blame himself even more.
4- Lastly from what I saw... King seems to be the true villain... evil, greedy and manipulative. So if they'd done it he'd use it against them somehow...
So while I agree that things would be so much better if mcs in general weren't so lenient with villains... in this specific case I understand their actions...
You could have killed the First Prince and elimiated the future villain but decides against so stupid.