[possiblywrong]

Author of the article here; this is a great point. This experiment initially stemmed from a nice analytical solution to the problem of computing the expected value (via generating functions as described in the post). Computing other moments, let alone the entire distribution, required some Monte Carlo simulation, as shown at the end of the first article (https://possiblywrong.wordpress.com/2019/01/09/identical-pac...) before I started the experiment.

And even this histogram assumes a distribution of total number of Skittles per pack (that varies) that I had to guess at beforehand. In hindsight, the final sample distribution suggests that I probably initially overestimated the true variance, and thus also overestimated the expected number of packs I would need to inspect. In other words, this experiment arguably took longer than "average."

So you're right-- this experiment could have extended into 700 packs, 800 packs... and still have been consistent with the assumed model, but I would have simply been in an unfortunate 90-th percentile possible universe where it took much longer than "average."