The 1878-S Seated Liberty half dollar is an interesting coin about which we know very little. It is currently priced at $23,500 in G-4. That's a lofty price for a Seated Liberty half dollar. It is more than Carson City dates and much more than any regular date. The 1878-S remains something of an unknown better date.
What little we can piece together about 1878-S is that it was a date probably stuck in the middle of the Morgan silver dollar transition at the San Francisco facility. The 12,000 mintage of the 1878-S strongly suggests that the production of the date was cut short. The year before San Francisco had produced 5,356,000 half dollars.
The 1878-S would be the last half dollar produced at San Francisco until 1892. In fact, no branch mint would produce a half dollar again until 1892.
San Francisco was still basically a frontier mint. There were not large numbers of collectors there. Once a coin from San Francisco reached circulation, the odds were not good that it would be pulled from circulation to be in the market today. The 1878-S may simply be a case where none of the factors that have produced supplies today worked.
That said, it is still an extremely high price in any grade for a San Francisco coin with a 12,000-piece mintage. The Philadelphia Seated Liberty half dollars of 1888, 1889 and 1890 all had mintages of 12,000 to 13,000, and they are a far cry from the high prices of the 1878-S. It's not always fair to compare coins from different mints, but you would expect some similarities here.
NGC has seen only nine examples of the 1878-S Six were Mint State. By comparison, the 1888, 1889 and 1890 have been graded 74, 75 and 61 times respectively. At PCGS the 1878-S has been graded just 22 times, and 13 of them were called Mint State. The 1888, 1889 and 1890 hav e been graded 124, 115 and 94 times respectively.
Realistically, the grading service totals do not support the current huge gap in terms of prices, but it cannot be forgotten that the 1888, 1889 and 1890 also have proofs. The availability of top quality examples may be even further apart than the numbers show. The combined total for NGC and PCGS is just 31 coins, and that is extremely low. Something happened to the 1878-S, since much of our current supply looks to be coins that were saved by someone as the coins were released.
There are not many possibilities. The 1878-S could have been melted. The coins could have also been exported, since half dollars were sent to China and Central America. That was especially true of San Francisco half dollars. We do not know what happened, but exportation is possible because, for some reason, the 1878-S half dollar is not around in the numbers we would expect.