To me, it defeated the greatest benefit of taking notes, which isn't being able to reference them but the fact that writing down important information seems to help with memory retention. If I'm having to think about structuring my notes, then that's less likely to happen.

In fact, might it be better to take unstructured notes, and then restructure them later?

That actually makes quite a lot of sense. Step 0: Take unstructured notes Steps 1-3: Cornell method

Personally, this is my preferred approach. I feel uncomfortable making final notes the minute I have just learned something new. It's like your bubble of knowledge has to expand and connect to other thoughts and ideas in your head, otherwise my notes feel so superficial and incomplete.