It is now well known that a random coin toss has 1/6000 probability of landing on its edge. So the out-dated model that a coin toss always land on either heads or tails with probability 1/2 is wrong. Further, it has also been revealed that the physical coin toss process is not random, but deterministic. So the coin toss should be described as a phenomenon in Newtonian dynamical systems, and the "randomness" comes from the sensitivity of initial data, so it is not really random at all.
Therefore it clearly does not fit into the definition of classical probability. Because if we are talking about the coin toss as a random event with 1/2 for either heads or tails, then this is taking conditional probability excluding the case of landing on its edge already.
While the heads and tails had a pedagogy advantage for being easy to understand, I believe this is not an appropriate example that should appear in the textbook. And we all know there are a lot of good examples in quantum mechanics.
So my question is, why we still mistaken coin toss to be an example of classical probability? To me this is almost the same as leaving the mistake to the next generation while science has proved it is not true.