Formally and technically Cucumber/SpecFlow doesn't require you to write a When-step or rather Given/When/Then's are just executed in the order they are written in the scenario. In that regard you don't need a When-step.
But, as Andy Waite wrote about, the When-step shows on the action or event that your system takes from the "Setup" to get to the new state that you verifies in the Then-step. In that regard a When-step should be present in every test (as you wrote: what are we testing otherwise).
That leaves your final comment; what about verifying just the setup (Given the system is started, Then the database is clean as a naïve example). In such scenarios the When-step could be skipped.
So, as always, it comes down to readability and understanding. Scenarios are written to make our thoughts about the systems behavior concrete and clear. Use the form that optimize for understanding and learning about the behavior in question.
Without thinking too hard on this I would probably guess that the general advice is to always use a When-step that makes the event or behavior very apparent and clear. I would shy away from implicit and hidden behavior when possible.
I hope this helps.