The problem with milk is there are too many options, whole, 1%, 2%, organic, soy, almond....this is why we don't provide it, because we don't want guests thinking 'oy, we hate this brand/category' of milk, and then they're unhappy and it goes to waste, its the same reason we don't provide wine, it's too personal of a taste choice. We also have mostly stopped leaving fruit because most guests don't eat it and then it has to be thrown out. We don't leave bottled water because it's wasteful, although we may get a Britta or other water filtration pitcher.
We always leave something, either on arrival or the night before guests leave, sparkling juice, croissants, cookies, small cake, etc. and that is on top of coffee, tea, hot chocolate, spices, oil and vinegar as well as condiments in the fridge.