Why does the discount rate no longer vary by region?
As you noted, Federal Reserve Banks originally set their own individual discount rates, but now the rate is uniform across the entire Fed System. This change reflects an increasing unity in national credit markets. In the 1910s, money and capital did not flow easily from one region to another, so it was possible for interest rates in different regions to diverge. So originally, there were small and temporary divergences in discount rates at different Feds.
Now, though, we have a national credit market with instantaneous flows of money across the country. In such an environment, divergent discount rates would lead quickly to credit flows from one District to another, and the divergent rates would not be sustainable. Hence, the single national rate that we have today.
Note: Provided by EquilibriaChat, courtesy of the Federal Reserve Bank of Richmond. Please read their disclaimer.