Any type of memory work is good for the brain, and learning more than one language is a lot of memory work.  Piano creates better students as well.  Again with piano there is an enormous amount of memory work.

Language learning can be onerous if taught in an old fashioned deductive fashion, as latin and greek were taught in English Public Schools, and still in some archaic language departments.  But language learning is natural to the brain in an immersion environment with one or two multilingual parents.  The younger the better, but kids are very plastic to language learning up to say 12-13.

I

wow!
I only knew one man who spoke 12 languages.
He had never set foot out of Taiwan, but spoke English with great ease.
The archaic way of learning languages did work—conjugating verbs, endless grammar. 
The children who have been in French immersion all of their school years can’t get government jobs because their French isn’t good enough, so at some point, every child learning language needs to learn proper grammar.

Language plasticity, meaning ease of acquisition, lasts until the early teens.

The immersion environment I referred to was a home situation with mutlillingual parents speaking with their children; not to so-called immersion programs in public schools.

Conjugating verbs and using correct grammar are not archaic, but they are necessary elements of language clarity. What is archaic is a formal deductive method of teaching languages as opposed to an inductive method where knowledge is introduced as needed with gradual increase in complexity, and mirrors the reality of immersion language learning, as a child does, with his parents, from novice to expert.

Oh!  I had a good laugh at myself, Charles—you meant 12—13 years of age, and not languages!
I did meet an elderly gentlement while visiting Taiwan who spoke 12 languages though.

I’m sure that your method mentioned works very well; however I’ve always been impressed with the (now seniors) who graduated from Ontario highschools during the time departmentals were still written (my husband and eldest sister to name two) and their French is just excellent, even though they weren’t imersed in French language.
When my husband and I were living in Switzerland, while he trained for a while, he said within a couple of days French was just like English, even though he was 15 years out of highschool.
Again, not to argue with you, but I believe firmly that a good structural base in any subject is what helps a person take off in the same.

I totally agree; especially once that youthful “plasticity” fades away.  But how is the structure presented? That is the key; my son took classical Greek at U of T, and the instructor expected everyone to be able to regurgitate massive matrices of word endings on exams, whereas precious little emphasis was put on reading, interpreting and translating texts.  In her view, you could either do it or you couldn’t, and she oriented to the students who could present the complete answer, then move on without helping the less experienced students through the steps.