To Panerai being a 'military' watch though it is undoubtedly a military 'style' watch.
IMHO, military items in general fall under the axiom, "necessity is the mother of invention". While there are exceptions, most military items are designed to get the job done oft times using the best materials available in terms of performance and practicality.
At the time the Panerai design originated, it met the specific needs of the Italian Navy--illuminescence, visibility and water resistance. The materials and design of the watch were 1940's 'high-tech'. The current production of Panerais may emulate this original design but I don't think they would function as well as the originals under the same conditions, i.e., the original radioactive material was far brighter and longer lasting than either the modern day tritium or luminova dials.
That said, even though tradition is alive and well in the military, and a Panerai could certainly be a military seaman or diver's personal choice of timepiece, I sincerely doubt either the modern day or original spec Panerais would be up to modern military issue specifications. The design is over 60 years old, the technology no longer 'cutting edge'. I daresay the microchip has allowed many more uses (altimeter, depth gauge, stopwatch, GPS, atomic clock sync., data storage) for a wrist worn device in addition to merely keeping time. Cost being another factor--you can replace a G-shock for the price of regulating a Panerai's ETA movement.