In carrying out any military operation, commanders-in-chief balance the potential benefits with potential short- and long-term harm to the country and its population.
In the case of "releasing US citizens from NK prisons" which are presumably secure and well defended. You would need a major military operation to take control of the area. Defend it against the obvious response from the NK army, extract the prisoners and get out. The immediate cost in lives lost would be significant. The NK military is well trained and armed, and would have the benefit of local knowledge and logistics. The long-term effects could include provoking nuclear warfare on the Korean peninsular, and involving Japan and China. The gains would potentially be some Americans get released from prison. While the costs aren't certain, nor are the benefits, as the prisoners may be killed in the release attempt or the Koreans may execute the prisoners when they realise they are under attack.
The diplomatic implications of using force are also mixed. Normalising the use of violence tends to result in more violence being used, and that would include other countries using force against the US.
In this case the cost-benefit analysis isn't too difficult. The costs of mounting such an exercise far outweigh the benefits.