Biotech Values

[iwfal]

I consider “noise” to be the bias caused when a trial is as balanced in all respects as a trial of the given size can be in practice, but still not perfectly balanced in a mathematical sense.

I would change the definition somewhat. Noise is that which, even in a perfectly(!!!!) balanced trial, causes the treatment to seem smaller in efficacy than it really is. The Chi Square example is a good one to illustrate this. Very close to perfectly balanced and yet it obscured the size of the treatment effect regardless of trial size.

Using this definition (which may be different from yours), “noise” for a trial is optimally balanced in a practical sense ought to decrease as the trial size increases.

I agree completely that the chance of an important imbalance goes down substantially as trial size increases. But this isn't about imbalance. Even in a perfectly balanced trial the noise has an impact on measured efficacy and p value. See Chi Square example. Really, the Chi Square example is very illustrative.