You do not need a full case framework every time you brainstorm, but some structure usually makes the answer much stronger. It helps the interviewer follow your thinking and it helps you generate a broader set of ideas without repeating yourself.
A simple approach is to name two or three buckets before you start. For example, if you are brainstorming ways to improve airline profitability, you might separate revenue ideas from cost ideas, then break those down further if needed. That gives the answer shape without making it feel overengineered.
The structure should serve the ideas, not become the main event. If you spend a minute building a complicated taxonomy before giving any ideas, you have gone too far. Usually one sentence of organization is enough.
Over time, this also makes brainstorming easier because you are no longer searching the entire universe for the next idea. You are moving through a few logical categories. A useful reference is structured communication throughout the case interview if you want to go deeper on that part.