The point of putting at least some of the cost on the people being rescued is to make sure more people don't go out dangerously and require rescuing in the first place. I don't know if it makes sense for them to fund the whole thing but I see the purpose of the incentive.
What other things in your life where you've not taken due diligence do we assess costs? If you want the fire department to come to your house have you had your monthly fire safety inspection? The list can go on and on.
Lots of insurance plans require some due diligence to actually be covered. If a driver is reckless, they could be on the hook for the full amount of damages.
If you want to take an apt analogy it would be the fire department does not come out and attempt to cut you out of your damaged car until they've checked your credit record first just in case it's deemed you were at fault or risky. That's not the way it works fire and rescue comes out and attempts to do their best to rescue you from your vehicle without caring who you are or if you can pay. Reclaiming of damages for personal property is not the business of search and rescue. So in the original situation the Coast guard doesn't care whether they save your boat when you send out a mayday they come and help which is what we want.
Saving someone and holding them accountable for the situation are not exclusive. The fire department might put out a fire and then the government could still fine or jail someone for negligent arson if they took the wrong risk.