Here's the devastating truth: people with a half-assed knowledge of CS but with good other skills (project management, communications, customer service, people interaction, etc.) can and will often make unarguably better software than people who just get the fundamentals right.

You can spend all your life building the perfect implementation of a crappy system, but that won't rescue it. Good CS fundamentals (even provably correct algorithms and implementations) has its place in the software craft but that place is a fairly small niche, not the top of the heap.

gathering requirements has more in common with psychology, sociology and communication skills than mathematics. to make good software, you need to know what it needs to do much better than your customer, unless it's a really small thing.

Correct. This does not oppose my original statement.

Math is not just arithmetic or geometry. Is also a way of thinking and a way to sort and structure your analysis. Which helps you to know how to use psychology to ask the right questions, which leads to understand what needs to be done better than the customer.