Randomized controlled trial and DAG In a DAG, why does a randomized controlled trial ensure there are no backdoor paths from treatment to response and hence no omitted variable bias?

Quite simply an RCT ensures no backdoor paths (technically it reduces the possibility of backdoor confounding to a chance which is inversely related to sample size) from outcome $Y$ to treatment $A$, because by definition random assignment $R$ is the only prior cause of treatment:
$$\boxed{R} \to A \to Y$$
In the simple DAG above, randomization is the only cause of treatment. If there were a backdoor path through some third variable like disease severity, or smoking history, then randomization would not actually assign treatment.
In this DAG notation, the box around $R$ (the randomizing process) indicates that it has no prior cause (i.e. it is a purely probabilistic phenomenon).
This specific fact about random assignment—that it reduces the role of confounding via a backdoor path to chance—is rather the entire point of random assignment to treatment.
