If a student in college wants to acquire a CS degree, they should be exposed to fundamental ideas in CS, not just what they'll need to be a professional programmer.
The field of computer science didn't exist when they went to college. They invented it, hence the awards.
Looking at building houses (just the construction side, not the mechanical systems), we have: - Architect - Structural Engineer - Architectural Technologist - Carpenter plus construction employees not officially certified. Each of these has a specific test, both written and practical (apprenticeship), and specific roles in the building process.
In software, we have no standardized tests, so companies substitute "BSCS" for "Software Engineer" in the requirements. And there is only ever one role officially defined; there is no separate "Software Programmer". Internally every companies has "Software Engineer I", "Software Engineer II", etc however this is rarely exposed in job postings and requirements and is never standard between companies.
The software industry could solve all this hand-wringing by creating a set of standardized roles, testing to create Certificates of Qualification for each, and getting HR departments to require these. And it would be possible, even with an established industry. Canada has added several new Professionals over the last decade, working with the existing industry to define the job, requirements, and build a phase-in plan that allowed the industry to continue operating.
Disclaimer: I am a professional engineer trained to design and build computers rather than program them.
It's a specific field within mathematics, with its own emphases and body of knowledge, much like how podiatry is distinct from general human physiology.
Really, though, all mathematicians specialize once they reach a certain level, for the same reasons all physicians specialize. It's just that you only happen to know the name of one of those specialties.