Actually, the agency can prescribe the fine, but any agency decision can be appealed to a court of law (usually through an administrative process). There, the case gets decided much like a tort civil case, with agency acting as plaintiff. Judicial rules will decide the outcome. Most likely, the kid's lawyer will initiate an appeal process, and the agency will likely settle with a minimus fine and some volunteer activity for the defendant. The fine will probably be a couple thousand, and volunteer activity will probably be a weekend or some such. The agency does not get to be judge and jury. If the kid refused to pay the fine and didn't try to negotiate or anything (non-responsive), then the agency would seek summary judgement against him in a court of law and go after him that way.

No agency can levy an insurance premium. What they can do (as with vehicle licensing agencies) is not provide a permit unless proof of insurance is obtained, thus ensuring that inadvertant expenses arising from permitted use are covered by the permittee, or the one enjoying the privilege at their own risk and expense, and not that of the general public. It seems to have been working out well for the privilege of driving a personal vehicle. It does make people accountable, more or less, for their own actions, at least financially. The cost of premiums could then be incentivised by certificates of training, longevity without an incident, deductibles, etc.

Hello, we've already been charging for rescue services! Who do you think pays the bill everytime that chopper heads for the hills, or the fire truck or ambulance gets called out? There may be volunteers, but someone is footing the bill for the use of the equipment, supplies, training, etc. When my house burned to the ground in 94, those firetrucks showed up even though I didn't ask for them (I happened to be out of town at the time). Should we wait to provide services until requested by the victim? As I recall, there was a payout from my insurance to the fire department for some services as well, which my premium paid for. Hmm, that seems reasonable to me, even though they didn't manage to save a darned thing (That's not a sarcastic statement either. I am glad they showed up and did what they did, I thanked them for it when they were done, too).

If we are not as a society going to lay the expectation of accountability on the heads of those who take the risks, then we certainly need to require some financial responsibility if the costs get excessive and the risks (both real and litigious) of the rescuers keeps going up. Letting the government handle financial responsibility like that has never proven to be an effective model, and invites the worst cases of corruption our history has ever experienced. Allow the government to regulate it, but keep the financial remuneration at the private level so the corruption can be at least lessened. It may not be ideal, but few things in life are. The reality is that you can only expect your neighbor to keep footing the bill for your foolishness for so long before he gets real tired of being broke at your expense.
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The ultimate result of shielding men from the effects of folly is to fill the world with fools.
-- Herbert Spencer, English Philosopher (1820-1903)