Capsid assembly is a good example if you want to make a macroscopic analog that works over less than geologic time, but the next step is for the assembled capsid to find and ingest a nucleic acid containing a viral genome as it floats around a broth containing all sorts of other nucleic acids.
It's wildly nonintuitive that this manages to happen. Maybe you're right, and it can be explained by the numbers being so tremendously large that they break intuition without the need to import any nonintuitive quantum weirdness.
But if so, isn't such an explanation problematic in its own right? It banishes:
> The quantum world is impossibly nonintuitive, and it's having an effect
in favor of
> The scales here are impossibly nonintuitive, and that's having an effect
Like... we're still shoving the explanation under a rug, it's just now it's a different rug. Either the quantum effects explanation or the large numbers explanation needs further development before we can call this phenomenon adequately explained, and rather than doing that development it seems like the whole field is dedicated to championing their favored side as-is.