Why Isn't Air Travel Governed By Admiralty Law?

In most material respects, air travel presents the same special legal concerns for substantially the same reasons as the aspects of travel by boat on the sea and navigable waters that gave rise to admiralty law.  The analogies were quite clear, and quite a bit of air travel pomp and circumstance (e.g. the title of the person who flies the plane and the understanding regarding his or her authority on that plane) consciously copy those of sea travel.  So, why hasn't admiralty been formally adopted as the governing law of air travel?

Part of the issue is that admiralty has grown arcane, rather than keeping up with modern trends, and even more importantly, not many lawyers are familiar with it.  Surely, the lack of lawyer familiarity also fostered the path dependent route by which the modern law of the air was developed.  The rise of the legislatively enacted statute, the Presidentially negotiated treaty, and governance by regulation rather than statute, all at the expense of common law innovation, surely played a part as well.

The one big substantive difference is that while sea travel historically involved long trips outside the authority of any land based court, air travel typically involves short trips from one land jurisdiction to another, and telecommunications mean that authorities on land are never truly unavailable or distant.  There is no need for an air crew to provide all of the elements of state authority for an extended period of time.
Does admiralty have anything to offer the law of the air, or visa versa?