The problem with restricting the use of the term “milk” is that people have been using the term “milk” to describe non-dairy liquids for longer than there have been trademarks. The word hasn’t ever been used exclusively to describe dairy.

Here’s a dictionary entry for “milk” from 1755:

https://johnsonsdictionaryonline.com/1755/milk_ns

Note that it includes almond and pistachio milks.