That's my takeaway from The Shallows by Nicholas Carr. Knowing how to derive information or where to find information doesn't mean you know the information and knowing the information is necessary to form higher level associations in the mind.
I memorized my multiplications tables like a good little boy, and I can do decent amounts of math in my head, but I am not a fast or as capable as the default calculator that comes with every smartphone on the planet.
I do agree that memorization is important, by the way. I just think that it's useless if you can't also derive your way there. Nothing wrong with having checkpoints in your mind though.
Education as a discipline has no real knowledge or skills in the Anglosphere beyond basic essay writing. Historically teaching was a craft, taught in trade schools or on the job, but for various reasons it moved to university without universitiea having of the content developed, so universities took the low road and asked PhD candidates to essentially write essays on the philosophy of education so that's now the content.
Those who can, do. Those who can't, teach. And those who can't teach, teach teachers, and since the content is just writing essays on the philosophy of education their confidence in non-existent abilities is never pressure tested.
For older kids, it can be a bit tricky, as their goals and opinions will matter a lot more, but look into evidence based study habits for exams, and help them get assignments done with a decently efficient process I guess.
They're not mutually-exclusive sets. In professional schools (law, medicine, perhaps others), some of the best-regarded instructors are successful practitioners who teach on the side.
In school I was tested on memorizing a map and drawing precise borders, rivers etc and various acronyms that were obsolete even at that time. They added 0 value to my education, except as unnecessary stress in having to memorize them. Similarly with being expected to memorize various physics and math theorems such that understanding was treated as having zero value (that is, if your wording isn't exactly the same as in the textbook, it doesn't matter if your answer is actually perfectly correct in terms of understanding). It was to the point of being prescribed several arbitrary essays to memorize, with one of them being randomly expected to be reproduced in an exam.
None of that added any value, most of it turned out to be hilariously divorced from real life expectations.
Even with your disingenuous example of language learning. People who argue that they don't need to learn the language because they can just use a translation app are making the point that they aren't interested in learning the language and have limited enough need to interact in it to get by with just a translator. Anyone who has actually interacted with a language they don't know understands that translation software doesn't obsolete knowing a language.
There was a slang term "refrigerator thoughts" that described someone staring into the refrigerator while thinking of a show plot and realizing there is a plot hole, a disturbing implication, etc. In any case, that's an example of insight. Hopefully we have these spontaneous realizations about less trivial things as well.
The more stuff you've got in your head, the more insights you'll have, which drive more questions whose investigations puts yet more stuff in your head.
I don't think you can split it. The critical piece is actually getting information into your head in the first place.