There are several issues I have with large refillable dispensers based on past experience. One is that sometimes due to the large quantity of the shower gel/shampoo, the product goes bad because most of these products have a shelf life after they are opened. If under sealed conditions, they can last quite long but once open they probably last 6 months to a year depending on temperature and humidity. I was using one of these products from an airport lounge shower and it felt kind of funny so I am kind of wary of using from them nowadays.
Another issue is the hygiene problem. Some of these refillable dispensers will have water seeping into the containers and that does not seem to be particularly hygienic after hundreds of guests who have used them prior. Though some newer ones might have improved on this problem.
Lastly, there is the issue of products being mislabelled or the staff at hotels or airport lounges filling the products onto the wrong bottles and mixing them up. I had this happen before as well where a product labelled as shampoo dispensed conditioners instead.
With these in mind, I always bring those small toiletry kits I take from past hotel stays whenever I travel. So I still hope that hotels continue with individual travel packs of amenity kits or give travelers the choice.