It's my understanding that in rescue missions where the targets don't pay with their lives, they end up paying monetarily afterwards.

Depends a great deal on who is doing the rescuing and whether the people rescued are considered negligent. Iceland's SAR team, for example, has gone back and forth on whether to charge people because when people believe they'll have to pay, they're less likely to call for help until the situation has gotten way worse and way more dangerous for the team.

The same would happen for the fire department. Can you imagine if an investigation blamed you for a house fire, then the fire department charged you for services? Many fewer people would call the fire department, and many more would die in house fires. People seem pretty casual here about wagging the finger. Just wait until they make an accidentally poor decision and need to be rescued.

In general, certainly at smaller scale (e.g. hikers who get lost/injured in winter, they're not charged in many places unless there was clear negligence. Which is mostly how you want it to be. You don't really want people to avoid search and rescue and just hope things work out because they're afraid of a big bill.