You don’t study in order to do independent research, studying is independent research. Private research is no research at all, it needs to be written out for the public.
Writing also gives a sort of scaffolding to the mind, helping it think inside a system. What’s not written is not likely to be remembered, and even less likely to be connected to other pieces of knowledge.
Written notes build a system of knowledge that can act as an extension of one’s brain itself. It is like your Second Brain, building connections between notes (thoughts) and gaining insights.