With bitcoin and other Nakamoto-consensus based crypto-currencies, the "solvency of the issuer" is irrelevant, because these currencies aren't debt based.
Or are you talking about fractional-reserve banking? If so, there's nothing that prevents implementing that on top of crypto-currencies and more than it can't be implemented on top of physical currency.
The fractional reserve system works precisely because only a few well known actors are allowed to create money -- which is a bit of antithesis for this kind of crypto currency.
However, I have to say that one of the things that bothered me (economically) about bitcoin is the lack of debt. This limits the availability of currency to either mining (which requires a large investment of hardware) or buying the currency on a market (which requires using a different currency and essentially relying on the same banking industry that you were trying to avoid). I would be very interested in seeing someone attempt some kind of monetary creation through debt in a cryto-currency.
You know who owns the Fed? Do tell.
That's... not quite how it works.
I can lend $20 or $2000 to a friend, and no money is created.
Money is created by aggregating a large number of relatively small accounts into a shared pot, and pretending that pot is larger than it really is (which you generally do by making loans out of that pot without telling any of the individual accounts that their available balance has gone down). Money is created by the possibility of bank runs.
If the borrowers all run off with the money, someone will be left holding the bag (or the empty pot). If you borrowed from yourself, that someone will be you.
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Bitcoin allows for debt exactly as much as cash allows for debt. There has to be something to make sure the borrower will (usually) pay back what's owed -- some concept of personal honor, risk of damaged friendships, legal liability and positive real-world identification, whatever. That mechanism is distinct from the currency used. That mechanism also probably can't allow for anonymity.
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setting up the rules for a fully distributed fractional reserve system would be non-trivial
There needs to be something at stake, which (1) the borrower can lose if they don't pay back the loan, and (2) is worth at least as much (to the borrower) as what was borrowed. There needs to be a reason to believe that a rational or mostly-rational borrower will pay back the loan.
There also needs to be some reason to believe that the borrower can pay back the loan.
Both of these are ties to external systems.
...getting back to the required shared pot, what does "distributed" mean here? Lack of central control over who can create the shared pots? A "marketplace" interface for finding shared pots to contribute to / borrow from? Automated selection of the "best" shared pot given your choice of criteria? A standard API for shared pots?
Oh, and the actual inability of the said central bank to bail out comercial banks by printing bitcoins.
Oh, and also the inability of a global superpower to manage its tremendous debt by playing with interest rates.