What the probabilistic approach misses is that the blockchain can split for other reasons, so the exponentially small chance of inconsistency is irrelevant. For instance, in 2013 the blockchain was split for 6 hours (24 blocks) due to a block with more than 10,000 transactions that different software versions handled incompatibly.
The other thing the probabilistic discussion skirts is that even with an exponentially small probability, you need to wait inconveniently long. A Ω value of 6 corresponds to 1 hour. To get down to "alpha particle" levels of probability you've got a much longer wait.
How is the nonzero probabilistic chance of a split not a problem considering that vendors are relying on the durability of transactions that may appear in one chain but not the other?
The other thing the probabilistic discussion skirts is that even with an exponentially small probability, you need to wait inconveniently long. A Ω value of 6 corresponds to 1 hour. To get down to "alpha particle" levels of probability you've got a much longer wait.