Today is the 50'th anniversary of Nixon's resignation. Here's the last lunch he ate at the white house (CW: Dairy)

You're close, but missing some details - the mass quantities of milk didn't come to be for no reason, it was a massive increase of production during WW1. The US made a shitload of condensed milk to feed both their soldiers, and, more importantly, exported a whole bunch of it to the Entente.

After the war demand naturally crashed but all the facilities and logistics for this production still existed, and the Department of Agriculture didn't want the dairy industry to crash, and they didn't want all that industrial capacity to go away in case of another war where they needed a bunch of condensed milk again.

So, they put out a big propaganda campaign promoting this stuff to home consumers, and naturally, this led to a increase in popularity for more normal forms of milk as well - this compounded on itself over the next few decades with additional advertisement campaigns - both government backed and those backed by the dairy industry - to promote milk more. By the 50s/60s milk-drinking reached it's peak, and because of the popularity over multiple decades it just kind of got culturally ingrained - particularly for children, but adults still drink a lot of milk too, although the numbers have been going down recently.

That's the big picture cultural reason - as a mayo American myself, I drink milk because I like the taste and texture.