> how we (the society) justify the shared costs incurred in searching for people involved in such a reckless mission

Nobody asked me if I want to pay for it or not. So i don’t feel that the “we” is justified. But if they would have asked me i would have voted to not move a finger unless some private entity (the company or the families, or literally anyone who wants to) pays for it.

They went out of their way to do something knowingly recklesly dangerous, and the cost of any rescue attempt is enermous.