I want this. As a vegan. and many other vegans too.
And no, you can't make milk with nuts. Nut, soya or rice milk is an imitation of milk.
You are not able to make proper cheese or higher with it. Current vegan cheese does not melt properly and has different taste. Those vegan milk alternatives are especially not very tasty with coffee.

And about "naturally"fallacy. Nut milk does not exist in nature. Nuts do. Same as yeast. To create nut milk, you need to process them. Then they also add other things to it to make it stable, not just water. Then they also fortify it with minerals.