I see one advantage in this setup, and several weaknesses.
Advantage: The ability to send fiat currency quickly to anywhere in the world assuming you have a network of 'fiat bankers'.
For sending and receiving funds, the fiat bankers network has no function. The fiat bankers only come into play when putting fiat on or removing fiat from the block chain. As an incentive, they can ask a fee for these transfers.
Weaknesses: The Bitcoin protocol was brilliantly designed to solve the problem of incentive to secure the network, with the reward being some of the value from the network. By unlinking the two, there is no incentive for securing the network (mining).
The incentive is still there: transaction fees that the miners, or rather: hashers receive when solving a block. This is equal to the situation that bitcoin will be in when all bitcoins are mined.
The other weakness is that you have security risk with the fiat bankers which you may solve, but it is very similar to the risk that exchanges pose at the moment.
Yes. But there are many ways to mitigate these risks, just as regular banks mitigate these risk: FDIC insurance, for instance, and traditional regulation. Also consider that regular banks require a much higher level of trust than a block chain based fiat bank would require.
The primary problem you seem to be solving is the volatility, and that can be solved more easily by having many exchanges like Coinbase, BTC-e, Bitstamp, and bitcoin ATMs.
If you don't want the volatility, hold fiat. When you need to send value -- Exchange to bitcoin, send, and let the receiver of the value decide whether to transfer back to fiat, or hold the value in bitcoin.
The fiat block chain transfers some of the advantages of bitcoin to fiat. For instance, the fiat on your address cannot be confiscated or frozen as it can when it sits in a bank account. In other words, a single person can no longer be singled out as a target to confiscation or account freezing. Also, it is more anonymous than a bank account if proper precautions are taken, just as with bitcoin in its current state.
Fiat and bitcoin (the currency/commodity) both have risk. Ignoring any security issues for the moment, fiat can be 'quantitatively eased' to a lower value (reduced purchasing power), while bitcoin currently has extreme volatility and the value goes up and down based on the news of the day.
Yes. This remains the main distinction between bitcoin and fiat, and which is my opinion bitcoin is superior to fiat as it can not be inflated. However, I find it interesting to note that some of the properties of bitcoin can be transferred to fiat as well.