Milk will be phased out because its carbon footprint is too heavy, so even if it will probably not disappear short-term, you cannot regard it as eternally a plentiful resource, and even right now it is starting to get a stench of non-politically correct (veganism, etc).
I sincerely wish you a great success!
It really won't. The food culture heritage of a large portion of the world won't be wiped out by an environmentalist/vegan dream. In the US there is a government finger on the scale which makes dairy quite inexpensive which might see a reduction, but carbon reduction is going to be primarily constrained to transportation and power generation.
You can have my cheese when you pry it from my cold dead fingers (unless you want some :) )
I just said it won't disappear, exactly for the reasons you quoted! (I know the subject, I come from a cheese-loving country)
But I'm still correct that it is less and less supported.
On the CO2e side, don't underestimate the sheer amount just from the cows.