So, what base should children learn to count in?
Or should they not learn how to count at all?
I personally have nothing against rote algorithms, or rote learning. It’s just a question of balance. Rote learning was dominant at one time, and so there was reaction against it to the point where it is now thought of as a thing evil in itself.
Also, of course, counting in any base is the same rote procedure. I actually taught me kids once, in the guise of a game, how to hand emulate repeated incrementation of a binary accumulation register using pennies. They caught right on and thought it was great fun, but I doubt they even remember doing it by this time.