It occurs to me that your argument 1 is set up strangely: it assumes perfect correlation between flips, which is not how a coin is assumed to behave. If instead you pre-pick different large uncorrelated digits for each flip, then the difference between the uncertainties disappears. It seems that similar correlations are to blame for the caring about the type of uncertainty in other cases, as well.
It occurs to me that your argument 1 is set up strangely: it assumes perfect correlation between flips, which is not how a coin is assumed to behave. If instead you pre-pick different large uncorrelated digits for each flip, then the difference between the uncertainties disappears. It seems that similar correlations are to blame for the caring about the type of uncertainty in other cases, as well.
I have no idea what you are saying here.