Those are basically the reasons you'd need grants, yes. And yes, it's possible to go another route, and do research alone or with few students, in which case you don't need many grants (perhaps any). In areas where not much grant money is available in the first place (pure mathematics, say), that is what people do by necessity.

The author of this post comes from an area, systems, where large-budget, many-student labs are the norm, partly because of the type of research, and partly just because the (relative to other areas) availability of funds means most of your colleagues are going the large-budget, many-student-lab route.