In our world of finite resources where unemployed people are being cut off from benefits, spending $200,000 (or whatever the cost was) on finding a kid who should NOT have been out there in the first place is an insult AND an injury to people who really NEED those resources.
First, what qualifies you to say she should not have been out there in the first place? Are you a sailor of sufficient experience to make expert commentary on her route, equipment, and chosen time of travel?
Second, some resources are finite, but this search and rescue did not consume even a drop in the bucket. An Airbus was sent 2000 miles in each direction; that's maybe 7-8 hours in the air, assuming they could home in the PLB and didn't need to search much. The fuel expended on such a flight is perhaps 1/30000th of that used every day during normal operations. The pilots' pay isn't all that significant (and if they're on salary, irrelevant). The cost of renting the plane's time would probably be substantial, but still small by government standards. So that only leaves the cost of diverting the fishing boat to pick her up----again, probably small by government standards.
Search and rescue is part of the government budget. They plan for it.