Drinking milk and consuming various dairy products (kefir, yogurt, cheese, etc.) are strongly associated with "steppe people" which were seen as barbaric (sometimes rightly so), so this perhaps explains some of the points in this post.
"Piquant dishes, stimulating the guests to dining, were chosen in preference; amongst cheeses, those from Sicily and from the town of Tromileia in Achaia [in Southern Thessaly http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0064:id=achaia-geo] were particularly liked; cakes sprinkled with salt (epipasta) were another important feature of the Greek dessert" p. 266
I was curious about milk and cheese consumption in Ancient Greece and found the following in the Everyday Life of Greeks and Romans (https://www.google.com/books/edition/Everyday_Life_of_the_Gr...) about Greek desserts: