I must quibble with some of the epistemological terminology here. Both "graphical explanation" and "geometric explanation" are not properly speaking explanations. They merely restate the original empirical observation in graphical or statistical terms, but do not explain why the tails-coming-apart phenomenon occurs. The "intuitive explanation" on the other hand does explain why the phenomenon occurs (i.e. the distributions of other factors influencing the outcome come into play). Similarly, "regression to the mean" is merely a restatement of the empirical observations in statistical language, which does nothing to elucidate the causes of the phenomenon. It should be obvious that the causes of regression to the mean in a series of coin flips and in inheritance of continuous characters are different: coins do not reproduce and we can't select them for better tails-to-heads ratio.
I must quibble with some of the epistemological terminology here. Both "graphical explanation" and "geometric explanation" are not properly speaking explanations. They merely restate the original empirical observation in graphical or statistical terms, but do not explain why the tails-coming-apart phenomenon occurs. The "intuitive explanation" on the other hand does explain why the phenomenon occurs (i.e. the distributions of other factors influencing the outcome come into play). Similarly, "regression to the mean" is merely a restatement of the empirical observations in statistical language, which does nothing to elucidate the causes of the phenomenon. It should be obvious that the causes of regression to the mean in a series of coin flips and in inheritance of continuous characters are different: coins do not reproduce and we can't select them for better tails-to-heads ratio.