From my understanding, all new money enters the market either 1) by the Fed lending it to banks, so the Fed essentially owns bonds in the exchange, or, 2) The Fed purchasing other financial assets. So for each new dollar, it is represented by some new security in the Fed's "vault". This doesn't sound like it's unbacked to me. Hypothetically, if the Fed and the dollar "went under" would there not be some obligation to distribute these securities among all dollar holders?
Furthermore, what is stopping the Fed from acting like a fund where each dollar represents a (very) small percentage of all securities in "the vault". To me, it seems like this would create a basis for value of the USD. If a USD-holder were able to trade in his dollar for tangible securities, would this not increase his confidence in the system itself? What's the reason the Fed doesn't operate this way?
Very interested in hearing more educated responses to this, thanks in advance.