I'm restricting milk (rather cocoa) for my kids first because I think it's food,

That's exactly why I let my kids drink it in unlimited quantities. Well, to be honest I let them drink just about anything (nonalcoholic) in unlimited quantities. But milk is so much more nutritious and less sugary (they drink it plain) than beverages they might choose instead.
While we're on the topic, or rather so far off topic I can't even see the tracks from here, can I ask you one more quick non-
New Yorker question? How do you introduce your kids to alcohol over there? Do you wait until they're 18 and then they just drink as older people do? Or do they drink at home at younger ages? I'm interested in your family, but also your culture in general.
The drinking age here is 21. But when we were in Europe last summer, my then 18-year-old was old enough to drink. And my 17-year-old, while not yet strictly legal, had absolutely no problem obtaining a mojito when the two went to the beach together in Barcelona, or buying a beer when he stopped into the corner bodega in France. I decided to play it when-in-Rome, loosening the rules for my younger son also, and let them drink a little bit, which they never do at home. They were very moderate: a mojito on the beach, a beer or vodka-orange juice late at night. My confidence in their alcohol use was actually increased over what it would be if I had banned it entirely and then had no idea whether, given half a chance, they might drink until they were blotto.
The other night my son and I went to my stepmother's for dinner. She, after asking my permission, poured him a third of a glass or so of wine. She's American but very Europhillic, and her husband is Hungarian. I had no problem with it. It seems a much better approach than the standard American approach to alcohol, to absolutely prohibit it until the magic age is reached, and then ... time to binge like crazy!!
In Wisconsin, about an hour's drive from here, the culture is somewhat different. The state was settled mainly by Germans, and there's a very bar-friendly, beer-friendly culture there. Kids accompanied by their parents can drink in bars in unlimited quantities -- until they're 18. Then they can't drink publicly under any circumstances until they're 21. Sound bizarre? It's because at 18 they're adults, as everyone in the country is, so their parents aren't in charge of them, but Wisconsin's drinking age is 21, as it is everywhere in the country, so they can't legally drink.
When I was a teenager, both the age of adulthood and the drinking age were 18 (i.e., like almost everywhere else in the developed world), but a few years later they raised the drinking age. The federal government did not force states to raise their drinking ages, but would not give federal highway funding to any state below 21. Thus, all states are now 21.