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.
Incoming pedantry: IIRC, Tolkien "only" invented two full languages, Sindarin ("Grey Elvish") and Quenya ("High Elvish"), if "full" means you could write a letter or have a conversation in it. He did create the foundations and some vocabulary for several others, like (as you mentioned) Dwarvish, and the Black Speech of Mordor, and Westron (a.k.a. the Common Speech), the language represented in the books by English (with "real" Westron words, names, etc. confined to the appendices): but I don't think he fleshed these out to the same degree he did the Elvish languages.
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.
He created Quenya and Sindarin as more or less complete languages, with detailed grammar, extensive vocabulary and several writing systems. They are both Elvish languages, descending from "proto-Elvish", so he carefully tracked their evolutions, sound changes. The other Elvish languages and dialects were mentioned and/or alluded to, but not developed in detail.
Next, there is a series of languages he has developed to a far smaller extent than the previous two. The best known examples are:
1. Khuzdul, or Dwarvish, which exists as only a few words and phrases, spoken and/or written in his works, plus some general grammar rules. The explanation for it not being more known is that the Dwarves were keeping it secret, and used other languages for talking to any non-Dwarves.
2. Black Speech, used by Orcs and other Sauron's minions. Developed by Sauron and also only present in a few sentences and words -- as well as, of course, the Ring inscription.
3. Adunaic, or Numenorean - the most detailed described human language, similar to Khuzdul in some grammar aspects.
And finally, he has used real world languages to "represent" Middle-earth languages. The best examples are English representing Westron - the lingua franca of the western Middle-earth - and Anglo-Saxon representing language of the Rohirrim, to show its relation to Westron. That said, in later years ye has started "developing" those languages more, inventing e.g. Westron words to replace the English ones used in the books (e.g. "Suza" for "Shire").
He was a philologist, and by all accounts a decent one. He played a lot with the evolution of his languages (how they turn into new languages and how languages interact within a multi-lingual population), not only with the languages themselves. He couldn’t have done that with a single language.
As an aside, I don’t think we could call his rough sketch of dwarvish as “full”. AFAIK we only know a couple of words of it. He did develop 2 elvish languages quite extensively, though (Quenya and Sindarin), and worked on several other dialects.
I wouldn't really call Orcish / Dwarvish 'full languages' - they aren't developed that much. However, the two major Elvish languages (Quenya and Sindarin) are both a lot fuller.
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