The issue isn't that "they" issue money. It's that they have an EXCLUSIVE FRANCHISE over doing so.
In a free market "they" can issue all the money they like. However, others can too. The market will decide which is better based on demand.
So, please stop the ephemeralism. CONCRETELY spoken, the simple solution is to remove the exclusive franchise. Our nation prospered quite nicely, thank you, when private issuers of money was permitted through 1928.
There's no reason to "end the fed." The Fed's EXCLUSIVE FRANCHISE must be ended. In a free market, the fed can do whatever the hell it wants (and go straight out of business) as long as the monetary market is denationalized.