The problem with this assertion is immediately obvious to me, though maybe not to you.
You assert that it is a circular dependency, but a DAG relationship (arguably the most common graph in nature, due in no small part to the laws of physics) will generate the exact same result.
And that is the issue. You see this apparent discrepancy and immediately assume circular dependency -- which would be hard to explain away theoretically. I see that and immediately see the consequence of a DAG, which also happens to be the thermodynamically favored pathway for molecular systems. Sometimes, things really are as complicated as they look.
"You assert that it is a circular dependency, but a DAG relationship (arguably the most common graph in nature, due in no small part to the laws of physics) will generate the exact same result."
In what way? The error-correcting mechanism _must_ be in place for the organism to survive at all. But that error-correcting mechanism is determined by the DNA itself. That is a cyclic, not acyclic, dependency. The DNA needs the enzymes, the enzymes need the DNA.