I used to work in the industry.
Yes, the cotton is there to keep the pills from moving around in shipping. In the old days of glass bottles, many consumers would scrutinize the contents for chipped pills and of course, there would always be some. Especially in the longer supply chains like Vancouver.
About the bottle size. There are several reasons. First is that, when you fill it, the tablets have not yet settled and you need room to fill it on an automated line. So you need extra. But that is not the most important reason.
The labelling requirements are generally what dictates bottle size. The type has to be a certain size and there are always new requirements. So, you need a bottle big enough for the type or you need those increasingly common wraparound labels.
Also, you generally use standard sizes for cost and line setup reasons. A 100ml bottle could be the standard and even if your contents are 85ml, you probably won't spend the money (which you pass along in the price) for a non-standard 85ml bottle.
And lastly, there is shelf presence. But that is truly a tiny consideration. There shelf difference between an 85ml bottle and a 100ml bottle is trivial. Except, you don't want your bottle looking smaller than the competition for the same count.
The test will be Friday.