You're just inventing hypothetical scenarios when the stats would all take this into account
That is your key error. When you have enough events, they take into account all the possibilities: older children, post-operative children coming out of sedation, serial dislodgers, poor intubation.
When you don't have enough events - over just eleven shifts, for example - one or more of these possibilities could skew things. A child with a difficult airway, a serial dislodger and fidgeter, even - depending on your definition of unplanned intubation - a child with infection and vomiting - can bring you up to four incidents in no time at all.
You can't ignore factors like this, count up totals, and call the results a statistical analysis.
It's true that there's never going to be much you can do with four events out of eleven shifts to prove guilt, but a like for like comparison of the four extubations with other events at Liverpool would quite possibly prove that the four were not such an anomaly.
There's lots of reading you can do on unplanned extubations, but even this one-page presentation of an NHS case study shows some of the complexities which mean that counting events just doesn't mean much.
https://qicentral.rcpch.ac.uk/wp-content/uploads/sites/9/2025/05/7945.pdf