For me the most useful thing about plan mode in Claude or Codex is not the plan, I usually barely read it, it's that it forces models to gather as much context as possible before implementing. Without plan mode models tend to implement wrong solutions because they are reading not enough context before writing code.
Another useful property is the readonly nature. I can easily let multiple agents plan in parallel without having to worry about annoying worktrees or conflicts and then I can come back to the plans later.
Of course this can be done with just another prompt, but that's exactly what plan mode is. It's nothing more than a predefined prompt in the harnesses with maybe some extra guardrails (that don't always work)