The exchange itself doesn't need to be particularly trusted; you could do a transaction either instantaneous and of low value, or some more complex protocol. There's also no inherent monopoly for the exchange, although there's a natural monopoly for any given pair of currencies.
Assuming everything is automated and low friction, you could be in and out of a given currency to make a transaction pretty fast, so arbitrarily short risk. You could split transactions up into smaller transactions so arbitrarily low financial risk per transaction.
In your described system, the issuers still face the fundamental problem of having to have a good reputation, but being unable to obtain this reputation in the standard way (real-world identity in a powerful "rule of law" jurisdiction), lest the delegator 'discourage' them from facilitating anonymous transactions. Multiple competing issuers do not help the situation due to the catastrophic failure mode of each - bank run and worthless currency.
Creating a widespread reputation that isn't derived from real-world identity is the problem that bitcoin is attempting to solve, which is why the novel part of it is solving a coordination problem and not a problem from cryptography.