Regarding the large amount of government $$$ likely consumed in the search ...
Remember, government assets (hardware, personnel, consumables) are used regularly for training purposes. At substantial $$$ cost and not-infrequently, cost of lives.
While this is is a bit of an edge case for SAR, it is not outside the scope of objectives (see all the commentary above about the original "find" of the Titanic as a side benifit of a clandestine government-sponsored, nominally private-sector mission and the earlier project Azorian/K-129/Glomar Explorer) that legitimately arise.
I certainly think that the US government has developed (and/or VERY MUCH wants) in-house capability to perform deep SAR capability without the NEED to bring in "private" assets - plausible deniability in clandestine operations aside.
Despite all the jokes and criticisms about the inefficiencies and sometimes questionable (from the outside at least) gov/mil decision making, there are some very smart, very dedicated career people in the ranks. There is a huge amount of knowledge to be gained from a real world deployment, and I expect that this event chain will be deeply reviewed. Both of, and at, the individual asset level, and at the systemic level. Sensing/intel, analysis, mobilization, equipment efficacy, etc.
I would not be surprised if an objective accounting down the road would report that the ROI is better than the training/testing cycles that it, at least could, replace.