Yes exactly, and your numbers are a lower bound, because the professor must do a few things: supervision of the PhDs, teaching (prep, lecturing, admin), grant applications, peer review (if not delegated to PhDs/postdocs) etc. The actual time the professor has for pure research is... not as much as you'd think.

Which means that having more PhD students means you can explore more of your own ideas by assigning them to it. It also means more teaching assistants and so on for your course. So the chances you will take and graduate one at a time are very low. Also, you know some fraction won't make it, so you need to account for that too.