TL;DR: The problem with math is that it is layers of abstraction. You need some familiarity (not just bare understanding) with one layer before you can progress. Most students don’t realise this and thus become frustrated when they fail to understand something even though it is clearly defined.
Many things have already been said, but I need to challenge your second assumption:
Rule out these non-answers because they also appertain to law and medicine.
Incrementalism. Law and medicine "also build on each other in a way that most topics don't, especially before college". Law schools make contract law a prerequisite for commercial or maritime law.
Incrementalism is no binary thing: All fields have some of it, but there is a wide spectrum from deep fields (with lot of increment) to broad fields (with a lot of content).
(Pure) mathematics is clearly on the deep side of this spectrum:
For example, you can be a number theorist by only being good at this one thing and knowing about a few related mathematical subfields. The number theory that doesn’t require depth has already been discovered millennia ago. By contrast, a general medical practitioner needs to know about a lot of common ailments and a bit about biology, chemistry, physics, pharmacy, psychology, bureaucracy, and mathematics.
This is exacerbated by the abstractness of mathematics. In fact, I would argue that the core of mathematics is not proofs, but finding the right abstraction to be able to formulate useful theorems and facilitate proving them. And this abstraction comes in layers on layers. The problem with this layered abstraction is that you have to be somewhat fluent in one layer to grasp the next one. Otherwise you quickly have too many things you need to mentally juggle at the same time.
Consider your example of integration: To understand what integration is, you need to have a clear understanding of functions (amongst other things). To understand functions, you need to understand variables. To understand variables, you need to understand numbers and elementary arithmetics. And the last things are already something on which most children spend the entirety of primary school. (Yes, we also teach them stuff like multiplying with pen and paper, but that’s only a means to the end of understanding numbers and multiplication, since pocket calculators can do this better than any human.) And university-level mathematics puts layers of layers on top of that.
By contrast, consider MRNA vaccines (i.e., some top-notch medicine). To understand how these work, you need to first understand what cells are and how DNA works. On this basis, you can continue to understand what MRNA does, how viruses work, and how the immune system works. There are some layers here, but only some and they are not that abstract. For example, you can see cells under a microscope and you can explain DNA by analogy to blueprints. I can understand these things without any university-level education on these matters, and I can even explain them to a child in primary school.
(Also see this XKCD.) Mind that I am far from being able to develop an MRNA vaccine myself, because I considerably lack breadth in medicine, pharmacy, molecular genetics, etc.
Now back to your question: Since mathematics requires you to wrap your mind around layers of abstraction, what determines your learning speed is how quickly you can understand abstract concepts and automatise them (so you can apply them without occupying too much of your brain). If you go too fast, you will inevitably hit a barrier where you run into something that is clearly spelt out to you, but you cannot understand because you just lack experience with the previous layer of abstraction. This is naturally frustrating, in particular if you do not understand why you are struggling (which is quite common because most professors do not realise or tell you these things; at least nobody told me). Something similar also happens in other deep fields, such as physics, philosophy, or linguistics.
By contrast, the limiting factor of learning speed in a broad field is the amount of stuff you can learn. You will hit barriers, but they are of a different and more obvious nature like bad explanations, being applications of another field, or you being tired from cramming too much knowledge into your brain since you last slept.