Not something everyone learns. My kids seemed to enjoy it. My older daughter learned quite a lot of algebra etc. by doing physics.
> learning the periodic table
You do not need to rote learn all of it, and you remember enough by learning about particular elements etc.
> basic language and alphabet skills
My kids learned to read through firstly reading with me (or others) so enjoying the story and learning words as we went and guessing words on flashcards. Then on to reading because they linked it.
Admittedly none of the above was in school, but my point is that its not intrinsic to learning.
> At some point in education with most fields, you will have to move beyond concepts and do some rote memorization and repetition of principles in order to get to higher level concepts.
Not a great deal and it does not feel like as much of a grind if you enjoy the subject and know where you are going.