You can remove Bob from the scenario and the problem still stands. Say that Charlie gets the IOU directly from Alice, David and Eve are left with duplicate IOUs. Alice has trusted Charlie with $10, not $20, so she can not re-pay both of the creditors. If you say "David and Eve should not have trusted Charlie then, so too bad if they lost each $10", consider the systemic issue if the double spending is made against with thousands of participants.
Without a way to control for double-spending, everyone can mint IOUs freely and any credit note is essentially worthless. And if remove the idea of IOU and try to make all transactions "cash-based", you just turned a fungible-currency into a non-fungible one (are these $10 coming from Alice-the-good-creditor or are they coming from Dick-the-double-spender?)
Without any transitive property, "Charlie gives his own IOUs" already exists. It is called "selling on credit". No crypto required. Shop owners have been doing that for centuries with pen and paper.
Alice wants to buy an apple from Charlie. Alice gives an IOU to Bob, Bob gives an IOU to Charlie, Charlie gives the apple to Alice.
And - sure, everything crypto does could be done with pen and paper and a phone line. But here Bob's computer can agree to do this without Bob's involvement.
Another thing, if you want to make transactions like the one you described, you don't need to pass IOUs around, you just pass money. Alice gives the IOU to Bob, Bob gives her money and then she can buy from Charlie, David, Eve or anyone else.
What is the scenario you're imagining of Alice attacking Charlie?
What you want to do is an digital version of Hawala. Hawala works, but there is a reason it is not automated. You can not scale it and it gets very easy to hit liquidity bottlenecks.
I think your ideas are in the right place (if you look at Raiden's off-chain side payment channels, it works somewhat similarly with what you are attempting to design) but can we agree to the fact that if they were feasible to be done without BFT mechanisms, it would have been done already? It is not like people want to use blockchains.
What are these liquidity bottlenecks? Feel free to reply with a link or a keyword if this is common knowledge.
One thing I like about this model is that you can have regular fiat money on top if Charlie gets his IOU from the US government and Alice gives one of US government IOUs back. But it can now be a single network for all currencies where anyone can start issuing their own money.
> can we agree to the fact that if they were feasible to be done without BFT mechanisms, it would have been done already? It is not like people want to use blockchains.
I'm not sure. Would anyone be able to profit from it? Developing the software and educating people is hard, especially with p2p things.
Re: profiting from the Blockchain, you are going at this backwards. You don't need to make it profitable by the tech. What we want is to have a global payment network that can make transactions cheaper than (and equally faster/secure as) Visa. If that were possible to do without blockchains, the market would pay handsomely.
If something happens to Bob, too bad. Both Alice's and Bob's IOUs are void because Bob can neither pay up nor demand payment. Both Alice and Charlie are sad because they knew Bob, and their ability to trade was more valuable than the current balance.