This is often a problem with dnd discussion that can create discourse. Based on how different we run our table and worlds.
In my world the guards are the patrolling force of city. They are there to create connections local people, throw out Barthus when she has drank to much. To collect information about Grazth boy that run away for the third time and bring her home from drydock. To deter people from trouble. But when it it looks like shit is about hit the fan, Ozloth comes in bloody claiming he saw Kobols in the pasture.
They call in cavalry that are adventure partys.
this loud bunch that came in to town with weapons, armor and training.
Because they expect adventure to be the swat team of my world.
Because you lose two guards because you want to seems big and scary is that really more intimating? Then having money to splurge to get adventure party to wipe out the bandit camp and still have your guards?
now to our sudden drop of department in our supposedly deadly fight against demon Morlucka the swamp king.
I would be weird but I would let them use all the power. If they convinced the department to come down and now they are 35 vs my 9 cultist that is how it is. I think it is a good win for them and I think the player would just think it a cool moment when they “tricked” the GM.
I don’t think would be worth prepping for stuff like that. I would just grab my guard stat block and just roll with it. But I understand completely for someone who prefer more prepare that would not be fun answering all the less fun questions.