Why? Everyone is only ever dealing with people they trust. And every single agent is in charge of confirming or rejecting every operation they agree to.
Alice trusts Bob, who trusts Charlie. Alice has no idea who Charlie is.
Now Charlie gets $10 dollars as credit (not the same as cash) from Alice (mediated through Bob) and wants to buy $10 items from David and Eve. He shows the letter saying that Alice is good for the cash. Without a distributed consensus method, how can David or Eve confirm that they will be able to go to Alice to collect the cash? How can they even know that Alice has the cash in the first place? What if something happens to Bob?
The only way to do this without a blockchain would require something like Paxos, but Paxos only works if the participants are selected a priori. Every new participant would have to be vetted by everyone else, or everyone else would have to follow some central authority that can grant access to the system. If you are going this route, you are just re-inventing a credit cooperative.
Charlie cannot get a 10$ IOU from Alice, he can only get it from Bob. If Alice wants to give a 10$ IOU to Charlie, she will have to give it to Bob and ask him to give an equivalent IOU to Charlie.
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.
I don't think you understood. The scenario I presented Charlie is malicious by making a double-spending attack against David and Eve, separately.
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?)
Charlie doesn't give Alice's IOU to David and Eve, he gives his own IOUs. He can default on those, but that's implied by David and Eve interacting with Charlie directly.
This is not at all what you said in your original comment, which implied transitive credit.
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.