This is why I like mathematicians - they create a model and analyze it without taking into account conditions of the real world... and suddenly come to a conclusion that doesn't make much sense.
As we know, block space is limited and confirmation of a single transaction depends on how many unconfirmed transactions are pending. Hence we can't use Poisson process that doesn't have memory. Hence your model can't be described as such a process. Try another model or extend the existing one.
No one is suggesting that there aren't other factors such as mining pools/miners rejecting Txs, certain blocks hitting the 1MB limit, users not including proper Tx fees, dynamically changing difficulty rate within the retarget, ect...
This doesn't negate the reality that the Poisson distribution still represents a very useful probability curve which matches most real world confirmation times within the bitcoin ecosystem. One could create a more sophisticated algo which anticipated other variables like difficulty adjustments but the probabilistic accuracy wouldn't be much more accurate than the Poisson distribution.
This does bring up a very important weakness of bitcoin because the average person is horrible with math and probabilities which leads to threads like this. Most Wallets in the future should mask or hide confirmation times from the everyday user and include more intuitive ways or showing the users that a transaction can be trusted. There are many ways to do this with interchannel payments, sidechains, pre-signed txs, looking at the memory pool, and/or a TaPoS layer.