I'm not sure if you're reading more into what I said than I intended, but I'm not convinced by this argument. You might have missed that this course was on security in general, not cryptography; not everything in the course was cryptographic related.
That said, I'd argue that for the vast majority of software engineers the type of stuff they're dealing with can be dealt with without needing to know the math. For example, you don't need to understand the math to behind the algorithms to know that bcrypt is a reasonable password hashing algorithm and that sha1 and md5 are not, or that salts are used to mitigate issues when users reuse passwords. These are principles that you can understand at a high level without fully understanding the underlying details. If anything, I think that overemphasis on requiring people to learn and understand the math has the effect of over-focusing on simpler algorithms that aren't actually what people want to be using in practice due to the fact that they're easier to teach and often foundational in conveying concepts that would need to be learned to understand the more complicated algorithms.
If using cryptographic algorithms directly requires knowing the math, then I'd agree that most people shouldn't be using them directly, but I'd go further and say that a lack of libraries that are safe for people to use for software engineering without understanding the implementation is a failing of the ecosystem; as much as "regular" software engineering people (like myself!) can struggle with the math behind cryptography, I think that a lot of people developing cryptographic libraries struggle with building reasonable abstractions and making user-friendly APIs (which is a skill I think in general is not emphasized enough for most software engineers, to the detriment of everyone).