I will try to share my experience regarding this question. Please note I am neither an educator or a mathematician. Take this opinion with a grain of salt. (Also, I hope this was not just some rethorical question)
1. I'd say "basic math" is a fairly complex beast. The difference being that children in elementary school are taught how to do math, not how or why math works. It is one thing to be set to memorize a collection of established facts (like multiplication tables), shown how to use those to solve some highly constrained problem (the typical pen and paper multiplication algorithm) and then set to practice the method (lots of multiplication problems for homework). It is a very different thing to be shown the definition of a concept (Abelian groups) and then thrown into a bunch of theorem proofs that "ought to make sense" on first sight (derive the properties of basic, grade school, algebra by the rules of abstract algebra).
2. An orthogonal point is that elementary school teachers have a more polished "culture" of how to transfer knowledge to students. They take many years to teach a relatively modest body of knowledge, starting from the most simple cases (addition and subtraction of natural numbers), and then extending to more general concepts (plus multiplication, plus division, plus squares&square roots, etc) and at the same time deepening the usages (natural numbers, integers, fractions, decimals, etc). Besides the core theme of arithmetic, additional concepts are introduced as permitted by the level of progress in this field (geometry, history and theory of numbers, numeric bases) and the foundations of the next big theme for middle tier education (algebra) are layered down.
Compare that to the ridiculous expectation of undergraduate level math classes, where every field is to be self contained within one (or at most two) term courses, and every session ought to introduce a new concept. University professors are able to get away with this because those courses are not a graduation requirement for most of the students, so most of those are allowed to fall from the back of the train and only the most talented, persistent and courageous ones succeed.
3. Then there is the students themselves. In general, even though individual dedication of children will vary according to both self curiosity and parental enforcement, it can be said that all children are expected to more or less grasp what is this arithmetic thing about. Children either do apply themselves or not, but they do not tend to question the need to memorize all those facts or practice those exercises. Once and adult student reaches university level math courses, it has been instilled in their brain that "memorization" is a debased form of intellectual pursuit and that they ought to be trying and looking for the underlying patterns in their subject of study. Armed with this false belief and under the pressure of unreasonable deadlines, the natural thing to do is to weasel out of the hard work required to truly appropriate a piece of knowledge and try to find some way to "get it" without actually "going through it all".