I think it's a kind of rope that frays on both ends for systemic reasons:
1. Students in math courses and their parents grow to prefer(through the overall institutional constraints) to have a simple exercise that guarantees them credit - while actually doing math is a matter of crossing the Rubicon into tough puzzle-solving, and it needs some guidance for unexceptionable students to start enjoying.
2. Math teachers, particularly in the lower grades where qualifications are lower, have a harder time teaching concepts than they do exercises. And they are also incentivized to hand out a grade, preferably one that satisfies the parents.
So no matter how the high level is set up, everything converges into giving the kids a worksheet to "plug 'n chug." Which is just a confusing, badly paced grind, and therefore an easy reason to hate math. Either you get it completely and are just sitting there chugging through the problem set, or you have no idea what's going on and it's due tomorrow so your grade rests on something you feel defeated by.
I actually think that for the parts that are currently treated as rote memorization work, the curriculum should lean into it and treat it like learning the alphabet, with worksheets where you literally fill in the dotted lines repetitively; hand them out to everyone as a portion of the homework. And then the logic and critical thinking aspects need to proceed like a philosophy course, with interaction through a step by step process, not "get the answer in the back of the book". This element is something I've long thought could be automated in some degree with computer systems that let you play with the concepts, and therefore correct your thinking.
