Can’t I purchase modern U.S. gold coins from my local bank?

You are referring to U.S. gold bullion which are coins issued by the United States Mint.  Their program is intended to offer a way for people to buy gold in the convenient form of coins while making money for the U.S. Mint.  This is the reason the coin's actual value is above the face value even when buying from the Mint.

Consider as an example the current $5 gold coin which contains 1/10 ounce of gold.  If gold is trading at $880 per ounce (the price at the time of this writing), the "melt value" of this coin would be $88.  Yet, you wouldn't see this coin available from The Mint at this price.  Rather, the coin has a premium added onto this figure to recoup the cost of minting the coins and make some profit).

These gold bullion coins cannot be obtained directly from your local bank because they are not intended for circulation.  These coins are intended to be socked away by investors and collectors.  Therefore, these coins are distributed directly from The Mint and from it's gold dealer network.