(My message) Why does the government pretend that different bills are issued by different FRB's? I don't see how it matters. They're all equally valid in all parts of the country. And it's not even like brand new bills sent to banks are 'issued by' the closest FRB. I once got some brand new bills that were from K (Dallas), >and I live in Rochester, NY. Wouldn't brand-new bills in my area be 'issued by' B (New York City) or C (Philadelphia)?
There's no "pretending" involved. The twelve FRBs are, to a significant extent, separate entities, which handle their own administration and keep their own books, balancing assets (mostly U.S. bonds) and liabilities (FRNs outstanding). The FRB of New York, for example, is a much much larger bank than the FRB of Minneapolis, and consequently is able to issue much more currency.
Of course, the FRBs also collaborate in substantial ways, sending representatives to the Board of Governors several times a year to determine common policies on interest rates and the like. But my point is that the system is deliberately decentralised: In a very real sense, the USA has twelve "central banks", not one.
Originally, each FRB did distribute only its own currency, so that (unless you lived near a district border) you'd rarely see out-of-district bills in circulation. Over the decades after the Fed's creation in 1913, though, several things changed. One was that people came to trust the whole Fed system much more than they might have originally, so that nobody any longer seriously wonders about what would happen if the FRB of Dallas went bankrupt or some such thing. Another was that travel about the country increased greatly, so that by the 1960s and 1970s the currency supply was getting mixed much more vigorously than fifty years earlier, and thus out-of-district bills were becoming a much more common sight.
Therefore, in 1983, the Fed and the BEP decided to simplify the currency distribution system to reduce costs. Nowadays, any newly printed FRNs may be shipped to any FRB. This doesn't really bother anyone, since it's no longer the case that people don't trust currency on an out-of-town bank. But the *quantity* of notes printed for each FRB still equals the number it issues, so that each bank's assets and liabilities still balance. (In recent years, the BEP's taken to streamlining its production schedule even more by printing large chunks of bills for each district in rotation, rather than skipping around a lot. So over a period of a month or two, there's no telling what sort of relative ratio the various districts will get; but if you look at the big picture, over a few years' time, you still see the pattern of big districts having many more notes printed than smaller ones.)