I saw a three cent nickel posted for sale by @lordmarcovan that sent me running to my Dansco to see if I needed to plug a hole.... Something occurred to me. Why did we only mint three cent nickels in Philadelphia?
In that era, all minor coinage was minted in Philly. The branch mints were exclusively designed to accept silver and gold deposits and mint them. If you look at other contemporary series (Shield and Liberty nickels, Indian cents), you'll notice none of them were minted in any branch mints either. The first were in 1908 when the new San Fran mint opened up. They began minting minor coinage there because the demand had grown too great for just the Philly mint.
Branch mints were established near where precious metals were mined (Charlotte, Dahlonega, San Francisco, Carson City, Denver) or imported in trade (New Orleans) to minimize the shipping risks involved in moving the metals to a mint. The shipping of minor coins from Philadelphia to where they were needed was a much lower risk. Also, specific to the three cent nickel piece, much of the nickel used at the Philadelphia Mint from 1856-on was mined in Pennsylvania. They knew how to handle it.
I think with the increased population on the west coast, the cost and inconvenience of shipping came into play. In the late 1800's, most of the demand for minor coins probably was within a few hundred miles of Philadelphia; by 1900, a considerable per cent of the population was out west. Shipping costs were not insignificant; even in the 1950's, catalogs would note "Prices higher west of the Rockies."
In 1890, just after the three cent nickel was discontinued, the entire population of California was just over 1.2 million.
I wonder if the opening of the Bingham Canyon copper mine in Utah in 1906 had anything to do with the decision to start making cents and nickels in SF? There was now a convenient source of copper for the SF mint, and remember, not only was the cent mostly copper, the "nickel" was 75% copper. And by 1910 the population of the Pacific and Mountain states was nearly 7 million; that is, one and a half times the population of the whole US at the time the Philadelphia mint opened.