When you signed up to rescue, apparently they skipped the part of your training which mentioned that you don't get to pick and choose whom you would prefer to help. If your career risks are not worth the reward or remuneration, there are probably a dozen other fields you're qualified to work in that don't require you to perform high-risk work for people you feel undeserving of the help your current job offers. No one in this world is forcing you to do what you're currently doing.
As for the specious claim that government has an obligation to its citizens, the Supreme Court has declared that law enforcement has no such obligation to any individual.
I'm not really sure how Somemedic's desire to pursue his career is irrelevant or incompatible with his getting pissed off at people who waste his time by putting themselves into dangerous situations out of ignorance, selfishness, or just plain idiocy.
Whether or not public safety and public service personnel have a "legal obligation" to protect the public, that is their calling and their job and it's the way they're utilized and the reason they're dispatched hither and yon, even in inclement weather. Beating up on such personnel who complain that their (limited) resources are being wasted on foolishness is too easy to do and also pretty much useless, as well as really taking out your ire on the wrong people.
The folks you should save your spleen for are the ones who put themselves into such situations, then cry to their elected officials that they weren't served well or properly or in a timely manner. Sure, most of us here on this particular forum can get around okay in bad weather or during a disaster (or at least have the sense to recognize our limitations and stay home) or have the resources to save ourselves if everything goes toes up. The ones you should take to task are the idiots who take no notice of their surroundings and then bleat about malfeasance when their own stupidity causes them inconvenience or physical harm.