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.
The "reaction" is mainly from unionized, affirmative-actioned teachers, many of whom are barely literate themselves, if they are literate. We can't know for sure, because we aren't allowed to test them.
Get rid of government schools. Make people pay to send their kids to school. Do that, and you can subscribe to any New-Agey education BS you wish.
You want your kids to know grammar; have them diagram sentences for the first four our five years of their language education.
You want them to have a basic grasp of math; have them memorize multiplication tables until they know them.
You want your kids to have high self esteem for no apparent reason, tell them that they already know everything they need to know and if something is hard, it's because it's useless.