The thing is, the definition of "milk" was never that narrow in the first place. Coconut milk is still being sold as "coconut milk". The white stuff that comes out of dandelions and rubber trees, I've always heard referred to as "milk". In Germany, we also have "Scheuermilch", which is a scouring agent that just happens to look white and viscous.

And ultimately, normal people do still call it "soy/oat/etc. milk", because I really don't think anyone's getting confused about that. Its function is like milk, not like cola. So, IMHO it should be enough to specify "goat milk" or "soy milk" or whatever.