I've had to deal with a similar issue for a product. We ended up summarising it in a fuzzy way that people's minds have a notion of 'micro' and 'macro' randomne

I've had to deal with a similar issue for a product. We ended up summarising it in a fuzzy way that people's minds have a notion of 'micro' and 'macro' randomness. In the case the coin flip, all heads or all tails is perfectly fine and will happen in macro random, ie if you took macro to mean > 1 million rolls let's say. But in micro random (the 12 rod we experience in real time) if that were to happen we'd feel uncomfortable and immediately assume it was cheated even if it was a product of true randomness because macro random suffers the same problems as very large numbers of slices of time