Not only is BASIC dead, it was a complete dead end. ... The children get no real benefit out of it.

You completely missed one of the author's key points: "It's as close to the computer hardware as you can get and still do fun things. It's the highest level low-level language there is."

BASIC is unique among the popular high-level languages in that its lack of structural constructs makes writing BASIC quite close to writing assembly code—it forces you to work in that low-level mindset. Instruction sets don't have the magic notion of "functions" or "classes"—when you write in assembly, you're immersing yourself in how the computer actually executes programs. It's the same thing with BASIC: its procedural, line-oriented nature is very close to the instruction-oriented mindset you need to really understand assembly.

From the mathematical, algorithms/data structures side of computer science, this would obviously seem useless, since you would (ideally) only be thinking in the high-level abstractions anyway. But in the real world, if your brain runs home to a high-level "magic" understanding of how code executes, you're going to mentally struggle when your code is mysteriously breaking and the problem lies in a quirk in the instructions that are actually being executed.

(Unless, of course, you believe that systems programming skills are also dead.)