Advice for preparing to apply and actually applying to science Ph.D. programs

I think this is good advice for some programs and professors, but not necessarily all. Some professors really are looking mainly for hardworking, competent research assistants, and all professors do want students who will produce research. But there's a large gradient from professors who emphasize the "student is an assistant" part, to professors who emphasize the "I am an advisor" part, and I think that's where the job analogy isn't always good.

Some professors have a huge, grant-funded project with deliverables already looming 3 years out, and they really are looking for something like employees. But some professors are looking primarily to mentor students who are capable of mostly-independent research, and in that case, things of the well-roundedness variety play some role, and your proposal of what exactly it is you want to do plays a big role as well (do you sound like you have an idea for a project, and will be able to pursue it, or are you waiting to be assigned one?). One heuristic is that professors who run large "labs" tend to want more employees, while professors who have 2-3 students want more independent researchers (often such professors are senior, and have their time taken up by all sorts of things that leads to them not having time to manage employee-type students).

Disclaimer: This might apply more to CS than to the natural sciences, due to the relatively lower cost of independent research in CS (your advisor usually doesn't have to buy you much in the way of equipment or experimental materials). Postdoc positions are also less mandatory in CS, so a bigger emphasis is placed on getting students who will be able to be independent, prof-position-worthy researchers within 4-6 years, since placing students in professorships brings prestige to the advisor. There's still definitely incentives tilting towards profs wanting employees, but there are also incentives for wanting to have proteges, since often that's how you really put your stamp on a field.