Writing one can be useful just because it helps clarify your idea. If you can't clearly explain what your trying to do and who its aimed at on paper then you should probably restructure your idea. You dont necessarily have to stick to a business plan format, something like the YC application form can be just as useful.

Of course a lot of the best stuff happens through accident/luck and no amount of planning will help you there.

In my limited experience, the best investors don't ask for biz plans. Perhaps instead of a biz plan being the method by which an investor judges an entrepreneur it is a means to adjudicate an investor.

The best employers don't require resumes, but it can still be useful to have one lying around.

Also, just because smart investors can create value for the business doesn't mean every investor has to be smart :-)