What I find interesting is that English speakers will rather invent a new language than use an already existing one. Klingon, Dothraki, the belter language in "The expanse" - all tv shows try hard to create something new. And I dont think politics is the reason here.
Tolkien also invented at least three full languages (Elvish, Orkish, Dwarvish). Though I believe he was well-versed in languages in the world so it's not learning laziness from his side.
Many of these were influenced by real languages: Sindarin by Welsh, Quenya by Finnish, and Dwarvish by (I think) Semitic languages. As you pointed out, he knew a lot about linguistics.
As for Orkish: I'm sure Tolkien makes a point of saying orcs had no language of their own; rather, they used a particularly crude form of the Common Speech, often peppered with words from the Black Speech. (This is the in-story reason why the protagonists in The Hobbit and The Lord of the Rings are able to understand and be understood by goblins and orcs.)
Anyway, none of this detracts from your point: invention of fictional languages does not imply a reluctance to get to grips with actual non-English languages, at least not in the case of J.R.R. Tolkien.
/end pedantry