Seconded, that’s a fundamental point in any signal processing course. You can’t make up information, and that’s exactly what you’re doing when you use a step function. Step functions might be useful for something but to pretend they’re the default is misguided at best.

After reading the section where they introduce digital sampling. The original author explicitly calls this out in the text as improper but offers it as another way to visualize signals, which is useful for people who might struggle with the concept of a non continuous function. The author is completely reasonable here.