Brian, thank you for your in-depth explanations here. I feel like I'm finally filling the most crucial gaps in my understanding, even if every answer leads to a new question.
However, I'm now quite confused about something: The fact that interest is paid on all reserves - not just excess reserves or those on deposit with the Fed - seems to defeat the purpose of IOR, because if banks get the "interest" payments from the Fed regardless of how they're using their reserves, doesn't that limit the effectiveness of IOR in regulating interest rates and lending? After all, "interest no matter what, as long as you don't bleed reserves" seems like a poor way of incentivizing any particular lending behavior. Clearly I'm misunderstanding something here...fill me in?
After all, it's not like the dollar is backed by gold in the sense of being redeemable for any fixed amount. That bygone policy previously gave the dollar value as a proxy for gold (which also led to expectations that it wouldn't be inflated). If FRN's were redeemable on demand at the Fed for a fixed quantity of some asset on the Fed's balance sheet (let's handwave the vague meaning of "quantity" for assets that aren't commodities like gold ), then the composition of those assets would obviously contribute to the value of the dollar, but as it stands, I'm having trouble seeing any real connection. In the absence of any kind of redeemability, the "backing" of the currency by the Fed's balance sheet just seems way too abstract (and disconnected from what the currency can actually be exchanged for) to matter, in and of itself.
Then again, taking the long view that the dollar is doomed to fail in the first place, I suppose the Fed's balance sheet composition might matter from the standpoint of switching over to another currency system. If another state-sponsored gold standard were ever implemented (which could be a terrible idea for a number of reasons), it would certainly matter whether the Fed's reserves at the end of this current system were composed of gold or toxic MBS's (and depending on the situation, I might be liable to value Treasuries closer to the latter ). The same might apply to any kind of switch to a regional or global fiat currency (God forbid), since the Fed's balance sheet could play a role in determining exchange rates and/or the US's stake in such a currency.