Perhaps we need to reflect on the purpose for which celestial navigation was developed...for the fixing of position of ships at sea, out of sight of land. In the middle of a four-thousand mile wide ocean an error of five miles is insignificant, and we realised this, but it in no way prevented us from being scrupulously accurate in our timing as much as our mathematics.
This was as true in the eighteenth century as it was in the twentieth, until the availability and reliability of GPS systems became such that resort to celestial navigation was considered no longer necessary. The US Navy no longer teaches it to officer trainees, but it survives due to the dedication of mariners of diverse backgrounds who learned the craft and wish to perpetuate it so it doesn't become a lost art.
It is prudent to reflect that in spite of all guarantees to the contrary, The US is perfectly capable of disabling civilian GPS signals, as are the Russians for their equivalent system. A guarantee that it will not be turned off is something only the foolish accept without at least one or two "grains of salt."
Celestial navigation can be viewed as a craft rather than a science, like wood-carving, or hand-thrown pottery. Certainly there are machines which will make more uniform products, faster and cheaper, but they are not hand-made products,with the flaws and imperfections that show their hand-made nature.
So too with position-fixing. GPS is clinically clean, swift and efficient...but the user is totally divorced from the stars, accurate time-keeping and "simple sums for simple sailors". I distrust technology basically because I have been using it since about 1977, and I know the errors and Achilles Heel of such systems. By all means let the mariner of today use his GPS receiver for fixing his position, but the prudent seaferer keeps one foot firmly planted in the past and uses his sextant to check the GPS. The sea is no respecter of technology, nor does it respect the works of man.
Celestial navigation also required the development of an accurate timepiece...accurate not in term of absolute accuracy per se, but inasmuch as its rate of deviation from Greenwich Mean Time was known and repeatable at any stage of the discharge of the mechanical escapement (the fusee detente) which powered it. Hence the development of the Marine Chronometer, a mechanical timekeeper with a rate which was more or less constant, relatively small, and for which allowance could be made.
Such importance was placed on accurate timing of sextant observations that a Chronometer Rate Book was kept on the bridge, and the deviation from standard time noted each day (in more recent times using a radio time-signal). At the annual Deck Survey, the marine surveyor would re-set the chronometer against standard time, and the rate-keeping would start anew. This was standard practice until I left the sea in 1992. All that had changed were our chronometers in their glass-topped recesses in the chart-table were quartz-crystal ones rather than the famous Frodshams, Mercers, Dents, Ulysse Nardins and Hamilton 21s of yesteryear.
These quartz marine chronometers are fantastically good rate-keepers. I have four such units, the best of which is a Seiko QM-10 which is only 8 seconds fast after 1470 days continuous running...a daily rate of 0.0054 seconds per day. My East German Glashutte is just 14 seconds slow after 847 days running, and the West German Wempe is 26 seconds slow after 1199 days, slightly worse than its cross-border counterpart. The poorest is a relatively cheap Tamaya, which is 20 seconds fast after 322 days...not all that good compared to the three others, but still far in excess of any of the best mechanical chronpometers. Even the iconic Hamilton 21, arguably the most technically-perfect, mass-produced fusee-detent marine chronometer ever made, is rarely able to attain a rate of less than half a second per day.
Mariners have a saying..."you can lend your wife but never lend your sextant."
A German C. Plath or Cassens & Plath sextant is truly a piece of ultra-precision equipment designed to operate in the hostile environment of salt-air, and varying temperatures. The Japanese Tamaya "Jupiter" and "Spica" sextants, beloved by the merchant marine around the world, are every bit as good in terms of manufacture, accuracy and usability.
The East German Freiberg sextants had greater errors along the tangent worm-screw in manufacture, but are also well thought-of as each came with a calibration certificate with the errors tabulated (as does any sextant worth keeping). They also came at a significantly reduced price and many mariners used them. British Hezzanith sextants are likewise extremely valued and accurate. There are Dutch Observator and French sextants, all of high quality. The Chinese have got in on the act and they produce a surprisingly good sextant (for the money) as the Astra IIIB, although the optics leave something to be desired when compared to German or Japanese sextants.
It is true to say all of these magnificent instruments are now in their twilight. But they will still work two hundred years from now...which cannot be said of any available GPS-receiver I know of. Modern electronics has a relatively short working-life. You only need to look at the long list of discontinued Garmin aviation GPS receivers of great popularity and usefulness to see the emphasis is now on frequent replacement instead of buying an instrument which will last your entire career.
In the middle of a vast ocean, a five-mile error in your fix is inconsequential. As you got nearer a coast and made landfall, visual bearings of landmarks took over, and a pilot (a man with local knowledge) was engaged to bring your vessel safely into harbour. Celestial navigation had served its needs for the mariner, and will continue to do so as long as there are mariners who continue to practice it.
However, in the aeronautical world it was a different mater. As aircraft speeds increased, and the need for extreme precision in navigation became paramount, the limitations of airborne celestial navigation became apparent, and drove the development of modern electronic navigation systems. This was inevitable, and as a result, airborne celestial navigation became a thing of the past - deservedly.
Those who choose to learn marine celestial navigation are keeping a connection to previous generations of mariners who went to sea in vessels of varying degrees of seaworthiness, manned with crews of varying competence, on voyages which had uncertain outcomes. One of the few certainties they had was the stars in the heavens, the navigational tables produced and checked by teams of mathematicians, and the easily-learned technique of measuring the height of a star above the horizon and from this (and the time of the observation), being able to draw a line on a chart and saying "we are somewhere on this line".